{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Basic Statistics in Python"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Statistical Analysis"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "from scipy import stats\n",
        "from scipy.stats import norm\n",
        "import math\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "# fix_yahoo_finance is used to fetch data \n",
        "import fix_yahoo_finance as yf\n",
        "yf.pdr_override()"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# input\n",
        "symbol = 'AMD'\n",
        "market = '^GSPC'\n",
        "start = '2014-01-01'\n",
        "end = '2019-01-01'\n",
        "\n",
        "# Read data \n",
        "df = yf.download(symbol,start,end)\n",
        "dfm = yf.download(market,start,end)\n",
        "\n",
        "# View Columns\n",
        "df.head()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  1 of 1 downloaded\n",
            "[*********************100%***********************]  1 of 1 downloaded\n"
          ]
        },
        {
          "output_type": "execute_result",
          "execution_count": 2,
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Open</th>\n",
              "      <th>High</th>\n",
              "      <th>Low</th>\n",
              "      <th>Close</th>\n",
              "      <th>Adj Close</th>\n",
              "      <th>Volume</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2014-01-02</th>\n",
              "      <td>3.85</td>\n",
              "      <td>3.98</td>\n",
              "      <td>3.84</td>\n",
              "      <td>3.95</td>\n",
              "      <td>3.95</td>\n",
              "      <td>20548400</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2014-01-03</th>\n",
              "      <td>3.98</td>\n",
              "      <td>4.00</td>\n",
              "      <td>3.88</td>\n",
              "      <td>4.00</td>\n",
              "      <td>4.00</td>\n",
              "      <td>22887200</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2014-01-06</th>\n",
              "      <td>4.01</td>\n",
              "      <td>4.18</td>\n",
              "      <td>3.99</td>\n",
              "      <td>4.13</td>\n",
              "      <td>4.13</td>\n",
              "      <td>42398300</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2014-01-07</th>\n",
              "      <td>4.19</td>\n",
              "      <td>4.25</td>\n",
              "      <td>4.11</td>\n",
              "      <td>4.18</td>\n",
              "      <td>4.18</td>\n",
              "      <td>42932100</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2014-01-08</th>\n",
              "      <td>4.23</td>\n",
              "      <td>4.26</td>\n",
              "      <td>4.14</td>\n",
              "      <td>4.18</td>\n",
              "      <td>4.18</td>\n",
              "      <td>30678700</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            Open  High   Low  Close  Adj Close    Volume\n",
              "Date                                                    \n",
              "2014-01-02  3.85  3.98  3.84   3.95       3.95  20548400\n",
              "2014-01-03  3.98  4.00  3.88   4.00       4.00  22887200\n",
              "2014-01-06  4.01  4.18  3.99   4.13       4.13  42398300\n",
              "2014-01-07  4.19  4.25  4.11   4.18       4.18  42932100\n",
              "2014-01-08  4.23  4.26  4.14   4.18       4.18  30678700"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 2,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df.shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 3,
          "data": {
            "text/plain": [
              "(1258, 6)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 3,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "new_df = pd.DataFrame({symbol : df['Adj Close'], market : dfm['Adj Close']}, index=df.index)\n",
        "\n",
        "# compute returns\n",
        "new_df[['stock_returns','market_returns']] = new_df[[symbol,market]] / new_df[[symbol,market]].shift(1) -1\n",
        "new_df = new_df.dropna()\n",
        "covmat = np.cov(new_df[\"stock_returns\"],new_df[\"market_returns\"])\n",
        "\n",
        "# calculate measures now\n",
        "beta = covmat[0,1]/covmat[1,1]\n",
        "alpha= np.mean(new_df[\"stock_returns\"])-beta*np.mean(new_df[\"market_returns\"])"
      ],
      "outputs": [],
      "execution_count": 4,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Beta:', beta)\n",
        "print('Alpha:', alpha)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Beta: 1.61279488\n",
            "Alpha: 0.0015127435601\n"
          ]
        }
      ],
      "execution_count": 5,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "close = df['Adj Close']"
      ],
      "outputs": [],
      "execution_count": 6,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Mean is the average"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "mean = np.mean(close)\n",
        "mean"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 7,
          "data": {
            "text/plain": [
              "8.164427659777418"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 7,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Median is the value of middlemost value"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "median = np.median(close)\n",
        "median"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
            "text/plain": [
              "5.0999999999999996"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 8,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Mode is the most frequent value"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "mode = stats.mode(close)\n",
        "print(\"The modal value is {} with a count of {}\".format(mode.mode[0], mode.count[0]))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The modal value is 2.28 with a count of 12\n"
          ]
        }
      ],
      "execution_count": 9,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Range is a measure of how spread apart the values are"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "range_of_stock = np.ptp(close)\n",
        "range_of_stock"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/plain": [
              "31.100001000000002"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Variance is a measure of how variable the data is"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "variance = np.var(close)\n",
        "variance"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 11,
          "data": {
            "text/plain": [
              "41.891972836178724"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Standard deviation is the square root of the variance and is measure how the data is spread out"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "standard_deviation = np.std(close)\n",
        "standard_deviation"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 12,
          "data": {
            "text/plain": [
              "6.4724008556469"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 12,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Standard error is the mean (SE of the mean) estimates the variability between sample means that you would obtain if you took multiple samples from the same population"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "standard_error = stats.sem(close)\n",
        "standard_error"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 13,
          "data": {
            "text/plain": [
              "0.18255669629927632"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 13,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Z-Scores measure how many standard deviations an element is from the mean"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "z = np.abs(stats.zscore(close))\n",
        "print(z)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 0.65113823  0.64341312  0.62332784 ...,  1.4408212   1.49180691\n",
            "  1.59068815]\n"
          ]
        }
      ],
      "execution_count": 14,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##  Contingency Table shows correlations between two variables"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "data_crosstab = pd.crosstab(df['High'], \n",
        "                            df['Low'],  \n",
        "                               margins = False) \n",
        "print(data_crosstab) "
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Low        1.610000   1.620000   1.650000   1.660000   1.680000   1.690000   \\\n",
            "High                                                                          \n",
            "1.690000           0          0          1          0          0          0   \n",
            "1.700000           1          0          0          1          0          0   \n",
            "1.720000           0          0          0          0          1          0   \n",
            "1.730000           0          0          0          2          0          0   \n",
            "1.750000           0          0          0          0          1          0   \n",
            "1.770000           0          1          1          0          0          0   \n",
            "1.780000           0          0          0          0          0          1   \n",
            "1.800000           0          0          0          0          1          0   \n",
            "1.810000           0          0          0          0          0          0   \n",
            "1.820000           0          0          0          1          0          0   \n",
            "1.830000           0          0          1          0          0          0   \n",
            "1.840000           0          0          0          0          0          0   \n",
            "1.850000           0          0          0          0          0          0   \n",
            "1.860000           0          0          0          0          0          0   \n",
            "1.870000           0          0          0          0          0          0   \n",
            "1.880000           0          0          0          0          0          0   \n",
            "1.900000           0          0          0          0          0          0   \n",
            "1.910000           0          0          0          0          0          0   \n",
            "1.920000           0          0          0          0          0          0   \n",
            "1.930000           0          0          0          0          0          0   \n",
            "1.940000           0          0          0          0          0          0   \n",
            "1.950000           0          0          0          0          0          0   \n",
            "1.960000           0          0          0          0          0          0   \n",
            "1.970000           0          0          0          0          0          0   \n",
            "1.980000           0          0          0          0          0          0   \n",
            "1.990000           0          0          0          0          0          0   \n",
            "2.000000           0          0          0          0          0          0   \n",
            "2.010000           0          0          0          0          0          0   \n",
            "2.020000           0          0          0          0          0          0   \n",
            "2.030000           0          0          0          0          0          0   \n",
            "...              ...        ...        ...        ...        ...        ...   \n",
            "27.400000          0          0          0          0          0          0   \n",
            "27.540001          0          0          0          0          0          0   \n",
            "27.709999          0          0          0          0          0          0   \n",
            "27.750000          0          0          0          0          0          0   \n",
            "28.110001          0          0          0          0          0          0   \n",
            "28.230000          0          0          0          0          0          0   \n",
            "28.270000          0          0          0          0          0          0   \n",
            "28.469999          0          0          0          0          0          0   \n",
            "28.530001          0          0          0          0          0          0   \n",
            "28.580000          0          0          0          0          0          0   \n",
            "28.830000          0          0          0          0          0          0   \n",
            "29.219999          0          0          0          0          0          0   \n",
            "29.930000          0          0          0          0          0          0   \n",
            "29.940001          0          0          0          0          0          0   \n",
            "30.590000          0          0          0          0          0          0   \n",
            "30.820000          0          0          0          0          0          0   \n",
            "31.830000          0          0          0          0          0          0   \n",
            "31.910000          0          0          0          0          0          0   \n",
            "32.200001          0          0          0          0          0          0   \n",
            "32.290001          0          0          0          0          0          0   \n",
            "32.419998          0          0          0          0          0          0   \n",
            "32.599998          0          0          0          0          0          0   \n",
            "32.630001          0          0          0          0          0          0   \n",
            "32.650002          0          0          0          0          0          0   \n",
            "32.779999          0          0          0          0          0          0   \n",
            "33.090000          0          0          0          0          0          0   \n",
            "33.230000          0          0          0          0          0          0   \n",
            "33.369999          0          0          0          0          0          0   \n",
            "33.599998          0          0          0          0          0          0   \n",
            "34.139999          0          0          0          0          0          0   \n",
            "\n",
            "Low        1.700000   1.710000   1.720000   1.740000   ...  30.250000  \\\n",
            "High                                                   ...              \n",
            "1.690000           0          0          0          0  ...          0   \n",
            "1.700000           0          0          0          0  ...          0   \n",
            "1.720000           0          0          0          0  ...          0   \n",
            "1.730000           0          0          0          0  ...          0   \n",
            "1.750000           0          0          0          0  ...          0   \n",
            "1.770000           0          0          2          0  ...          0   \n",
            "1.780000           0          0          0          0  ...          0   \n",
            "1.800000           1          0          0          0  ...          0   \n",
            "1.810000           0          0          0          0  ...          0   \n",
            "1.820000           0          1          0          0  ...          0   \n",
            "1.830000           0          0          1          0  ...          0   \n",
            "1.840000           0          0          1          1  ...          0   \n",
            "1.850000           0          0          0          0  ...          0   \n",
            "1.860000           0          0          0          0  ...          0   \n",
            "1.870000           0          0          0          0  ...          0   \n",
            "1.880000           0          0          0          0  ...          0   \n",
            "1.900000           0          0          0          1  ...          0   \n",
            "1.910000           0          0          0          0  ...          0   \n",
            "1.920000           0          0          0          0  ...          0   \n",
            "1.930000           0          0          0          0  ...          0   \n",
            "1.940000           0          0          0          0  ...          0   \n",
            "1.950000           0          0          0          0  ...          0   \n",
            "1.960000           0          0          0          0  ...          0   \n",
            "1.970000           0          0          0          0  ...          0   \n",
            "1.980000           0          0          0          0  ...          0   \n",
            "1.990000           0          0          0          0  ...          0   \n",
            "2.000000           0          0          0          0  ...          0   \n",
            "2.010000           0          0          0          0  ...          0   \n",
            "2.020000           0          0          0          0  ...          0   \n",
            "2.030000           0          0          0          0  ...          0   \n",
            "...              ...        ...        ...        ...  ...        ...   \n",
            "27.400000          0          0          0          0  ...          0   \n",
            "27.540001          0          0          0          0  ...          0   \n",
            "27.709999          0          0          0          0  ...          0   \n",
            "27.750000          0          0          0          0  ...          0   \n",
            "28.110001          0          0          0          0  ...          0   \n",
            "28.230000          0          0          0          0  ...          0   \n",
            "28.270000          0          0          0          0  ...          0   \n",
            "28.469999          0          0          0          0  ...          0   \n",
            "28.530001          0          0          0          0  ...          0   \n",
            "28.580000          0          0          0          0  ...          0   \n",
            "28.830000          0          0          0          0  ...          0   \n",
            "29.219999          0          0          0          0  ...          0   \n",
            "29.930000          0          0          0          0  ...          0   \n",
            "29.940001          0          0          0          0  ...          0   \n",
            "30.590000          0          0          0          0  ...          0   \n",
            "30.820000          0          0          0          0  ...          0   \n",
            "31.830000          0          0          0          0  ...          0   \n",
            "31.910000          0          0          0          0  ...          1   \n",
            "32.200001          0          0          0          0  ...          0   \n",
            "32.290001          0          0          0          0  ...          0   \n",
            "32.419998          0          0          0          0  ...          0   \n",
            "32.599998          0          0          0          0  ...          0   \n",
            "32.630001          0          0          0          0  ...          0   \n",
            "32.650002          0          0          0          0  ...          0   \n",
            "32.779999          0          0          0          0  ...          0   \n",
            "33.090000          0          0          0          0  ...          0   \n",
            "33.230000          0          0          0          0  ...          0   \n",
            "33.369999          0          0          0          0  ...          0   \n",
            "33.599998          0          0          0          0  ...          0   \n",
            "34.139999          0          0          0          0  ...          0   \n",
            "\n",
            "Low        30.510000  30.540001  30.639999  30.910000  31.200001  31.389999  \\\n",
            "High                                                                          \n",
            "1.690000           0          0          0          0          0          0   \n",
            "1.700000           0          0          0          0          0          0   \n",
            "1.720000           0          0          0          0          0          0   \n",
            "1.730000           0          0          0          0          0          0   \n",
            "1.750000           0          0          0          0          0          0   \n",
            "1.770000           0          0          0          0          0          0   \n",
            "1.780000           0          0          0          0          0          0   \n",
            "1.800000           0          0          0          0          0          0   \n",
            "1.810000           0          0          0          0          0          0   \n",
            "1.820000           0          0          0          0          0          0   \n",
            "1.830000           0          0          0          0          0          0   \n",
            "1.840000           0          0          0          0          0          0   \n",
            "1.850000           0          0          0          0          0          0   \n",
            "1.860000           0          0          0          0          0          0   \n",
            "1.870000           0          0          0          0          0          0   \n",
            "1.880000           0          0          0          0          0          0   \n",
            "1.900000           0          0          0          0          0          0   \n",
            "1.910000           0          0          0          0          0          0   \n",
            "1.920000           0          0          0          0          0          0   \n",
            "1.930000           0          0          0          0          0          0   \n",
            "1.940000           0          0          0          0          0          0   \n",
            "1.950000           0          0          0          0          0          0   \n",
            "1.960000           0          0          0          0          0          0   \n",
            "1.970000           0          0          0          0          0          0   \n",
            "1.980000           0          0          0          0          0          0   \n",
            "1.990000           0          0          0          0          0          0   \n",
            "2.000000           0          0          0          0          0          0   \n",
            "2.010000           0          0          0          0          0          0   \n",
            "2.020000           0          0          0          0          0          0   \n",
            "2.030000           0          0          0          0          0          0   \n",
            "...              ...        ...        ...        ...        ...        ...   \n",
            "27.400000          0          0          0          0          0          0   \n",
            "27.540001          0          0          0          0          0          0   \n",
            "27.709999          0          0          0          0          0          0   \n",
            "27.750000          0          0          0          0          0          0   \n",
            "28.110001          0          0          0          0          0          0   \n",
            "28.230000          0          0          0          0          0          0   \n",
            "28.270000          0          0          0          0          0          0   \n",
            "28.469999          0          0          0          0          0          0   \n",
            "28.530001          0          0          0          0          0          0   \n",
            "28.580000          0          0          0          0          0          0   \n",
            "28.830000          0          0          0          0          0          0   \n",
            "29.219999          0          0          0          0          0          0   \n",
            "29.930000          0          0          0          0          0          0   \n",
            "29.940001          0          0          0          0          0          0   \n",
            "30.590000          0          0          0          0          0          0   \n",
            "30.820000          0          0          0          0          0          0   \n",
            "31.830000          1          0          0          0          0          0   \n",
            "31.910000          0          0          0          0          0          0   \n",
            "32.200001          0          0          1          0          0          0   \n",
            "32.290001          0          0          0          0          0          0   \n",
            "32.419998          0          0          0          1          0          0   \n",
            "32.599998          0          0          0          0          0          0   \n",
            "32.630001          0          0          0          0          0          1   \n",
            "32.650002          0          0          0          1          0          0   \n",
            "32.779999          0          0          0          0          0          0   \n",
            "33.090000          0          1          0          0          0          0   \n",
            "33.230000          0          0          0          0          0          0   \n",
            "33.369999          0          0          0          0          1          0   \n",
            "33.599998          0          0          0          0          0          0   \n",
            "34.139999          0          0          0          0          0          0   \n",
            "\n",
            "Low        31.600000  31.719999  32.189999  \n",
            "High                                        \n",
            "1.690000           0          0          0  \n",
            "1.700000           0          0          0  \n",
            "1.720000           0          0          0  \n",
            "1.730000           0          0          0  \n",
            "1.750000           0          0          0  \n",
            "1.770000           0          0          0  \n",
            "1.780000           0          0          0  \n",
            "1.800000           0          0          0  \n",
            "1.810000           0          0          0  \n",
            "1.820000           0          0          0  \n",
            "1.830000           0          0          0  \n",
            "1.840000           0          0          0  \n",
            "1.850000           0          0          0  \n",
            "1.860000           0          0          0  \n",
            "1.870000           0          0          0  \n",
            "1.880000           0          0          0  \n",
            "1.900000           0          0          0  \n",
            "1.910000           0          0          0  \n",
            "1.920000           0          0          0  \n",
            "1.930000           0          0          0  \n",
            "1.940000           0          0          0  \n",
            "1.950000           0          0          0  \n",
            "1.960000           0          0          0  \n",
            "1.970000           0          0          0  \n",
            "1.980000           0          0          0  \n",
            "1.990000           0          0          0  \n",
            "2.000000           0          0          0  \n",
            "2.010000           0          0          0  \n",
            "2.020000           0          0          0  \n",
            "2.030000           0          0          0  \n",
            "...              ...        ...        ...  \n",
            "27.400000          0          0          0  \n",
            "27.540001          0          0          0  \n",
            "27.709999          0          0          0  \n",
            "27.750000          0          0          0  \n",
            "28.110001          0          0          0  \n",
            "28.230000          0          0          0  \n",
            "28.270000          0          0          0  \n",
            "28.469999          0          0          0  \n",
            "28.530001          0          0          0  \n",
            "28.580000          0          0          0  \n",
            "28.830000          0          0          0  \n",
            "29.219999          0          0          0  \n",
            "29.930000          0          0          0  \n",
            "29.940001          0          0          0  \n",
            "30.590000          0          0          0  \n",
            "30.820000          0          0          0  \n",
            "31.830000          0          0          0  \n",
            "31.910000          0          0          0  \n",
            "32.200001          0          0          0  \n",
            "32.290001          0          0          0  \n",
            "32.419998          0          0          0  \n",
            "32.599998          0          1          0  \n",
            "32.630001          0          0          0  \n",
            "32.650002          0          0          0  \n",
            "32.779999          0          0          0  \n",
            "33.090000          0          0          0  \n",
            "33.230000          1          0          0  \n",
            "33.369999          0          0          0  \n",
            "33.599998          0          0          1  \n",
            "34.139999          0          0          0  \n",
            "\n",
            "[728 rows x 705 columns]\n"
          ]
        }
      ],
      "execution_count": 15,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Scatter plot shows two variables that plot along two axes and it shows correlation or not"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(df['Adj Close'], df['Open'], alpha=0.5)\n",
        "plt.title('Adj Close vs Open')\n",
        "plt.xlabel('Adj Close')\n",
        "plt.ylabel('Open')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 16,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Regression is a measure of the relation between the mean value of one variable (e.g. output) and corresponding values of other variables"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "\n",
        "X = np.array(df['Open']).reshape(1258,-1)\n",
        "y = np.array(df['Adj Close'])\n",
        "LR = LinearRegression().fit(X, y)\n",
        "LR.score(X, y)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 17,
          "data": {
            "text/plain": [
              "0.9967102090185268"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "LR.coef_"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 18,
          "data": {
            "text/plain": [
              "array([ 0.99734456])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 18,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "LR.intercept_"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 19,
          "data": {
            "text/plain": [
              "0.019967673234484451"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 19,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "LR.predict(X)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 20,
          "data": {
            "text/plain": [
              "array([  3.85974423,   3.98939903,   4.01931936, ...,  17.40368338,\n",
              "        17.50341883,  18.12177146])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 20,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Elementary Probability Theory the outcome that could happen"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Monte Carlo method is an experimentals of computational algorithms that rely on repeated random samples. "
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "df['Returns'] = df['Adj Close'].pct_change()\n",
        "df['Returns'] = df['Returns'].dropna()"
      ],
      "outputs": [],
      "execution_count": 21,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df = df.dropna()"
      ],
      "outputs": [],
      "execution_count": 22,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "values = []\n",
        "S = df['Returns'][-1] #Starting stock price \n",
        "T = 252 #Number of trading days\n",
        "mu = df['Returns'].mean() #Mean\n",
        "sigma = df['Returns'].std()*math.sqrt(252) #Volatility"
      ],
      "outputs": [],
      "execution_count": 23,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(10000):\n",
        "    # Create list of daily returns using random normal distribution\n",
        "    daily_returns=np.random.normal(mu/T,sigma/math.sqrt(T),T)+1\n",
        "    \n",
        "    # Set starting price and create price series generated by above random daily returns\n",
        "    price_list = [S]\n",
        "    \n",
        "    for x in daily_returns:\n",
        "        price_list.append(price_list[-1]*x)\n",
        "\n",
        "    # Plot the data\n",
        "    plt.plot(price_list)\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
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1BAC3z7b0bWxeVszPzy8n83opM9tQaXU5+Vh/B29vb2H6aURfS1Yp7Zp9wvFcLseuXbswzZOJ6PcVqpwXDixviGpMFoiqlnNlcdzqIxuw3C+TYRdrtp2NKSWtAR1XMUtmahYU1xMsfYDDpRqGhHPDJ0U/XUvz8V9/nD+5/U/QpU5v0KoW+5buS3ld104ymo5HwneO6NwamARA1fp4Y8PLtrxBxTvIeNEa//0/OXFa9+/ZYIu+jc0LgEwmQ7lc5oYbbuAXv/gFL/UKcmlVZ73fw98PdTHo91DQjeU0CU9G6d4ZCrdNYFZXpik4ePAgd999N/fea6UpLmg6I9X6CtdOY6JAVFoTQG5uAYRgRrfSIlQUWPd7f8Dlm03W9wSRQqGcWoBw15Na+ksbvJZEX0rJh371Ie6dvpejGStrfF+oDykl5d/MUd29QFYziBrgCuj0ztyN3nAj1pxLh6Hw9UdqhA2J07Rq4+ra6ldRsUXfxuZ5xjRNvv71r/O5z32OdDoNwP79q59i9/kkpWq0ui3/dZ/Xyic/23jyvDPSlNSPW1ky9VxjxXv5vBV1s2vXLmZnZznQ3IB16iKuOlGgvcP6u5xK4Q9GGMta/QT0Khm/n7MjM1S8HZgeH4XEPIR7oPBE0X+4UKHH4yLutiaNY9ljjORG+MSFn+CSnkus6wn1YWTqyJqOlqySVTW2lWaI56+CkTsozTjxnXU2VcN6+uhtCHyyBYkkGDtzYatPhS36NjbPM/l8nnq9jsfjYfPmzWzatImDBw+i609t+b7YyWj6snAuif6vb7uVm2+26i+ZqkHyq4dQZ0qo00XMqnUv9Gx9RT/5fJ729nZcLhePPvooewtVzpk5wUQzkZqpGmiLVeI9YQDUUg6v6mM8XaG9YfKjx/6aoZ+/B4qzVPwxhCdAenISQl1QXljxWf90Yo5fZgrsCOr844P/iGEa3DF5B07h5Mr+K/nUxZ/iny/+Z7qCXaizzRBUQ5Kpabx18U7AoL7pL0kdCuE7+yyqNR1NSnrKBk7DenIIRl8YNXJtbGxWkSXr/h3veAdXX30127dvp1qtsrCw8DRnvjhIqRr/OZtaTmCmm5KsZtDmsiz9NV43wXqV1LGjjI2NAaDNl1EnCtSPZ6kPZ5eVysg9uehv3LiRw4cPsy9fZFM+ycToKPV6HT1VAwnhzgBeRYCoEAzGmHHD1aVhdhSP0LXwCEiTqieIyx2iVilSdbZBaeX9/6/5NLoEpXgPPzvxM/Ys7OEXE7/gou6LiHqjRNUQr02cjzQl6szJfQeZuspl2XvQwzsoZXswNCfebduoVXSqJvQUdZy6ExAEbNG3sXnpsyT6bW1WvPdSEY6leqsvdr48neIfTswx2YzFzzR9921N907M5eCchUmQkkKhgK7raAtWcRI9U6cxVcTdF0b4nCssfdM0KRaLRKNRzjrrLOr1OqmJCcJlKww0kUigpyx3jyvup9XpQJRyOLesIeET/EHmejRxMkSyrDvxBqzkaOmGH9QyNCzxrhkmdVPiUwQTyV8BcO1D15KoJLhq3VXW+Q/MU7htwpqwZkq4+0LgEHTnj9KpzWF0v4n6wUO41w7hCAapl1VqpqS/aODRJHWXIBuyo3dsbF5S5PP5J7ht0uk0fr9/ubpSNGot6mUymed8fGcaKSU3p3IAzDcs0U83RT/eFH0hBBsXZzAcluDlcjm0BUustXQNbaGCqyuAs8WzwtIvlUqYpkk0GmXt2rW4PB565iZRVMtfPz8/j5asggBnm492Q0XRVL5hCHQB61P3c2jDH5N2Wfe71NCJxKwY/XRZND/EiutPNKOLXAJmSzP4nD7mynOsi67jiv4rAGicsK6zeiiNOl/G3R+Gdj/nFaz1GXPg9dQeewzfWWcDUK9oVE3JuqqJW5MkIw7+ppDCfJri7M8WW/RtbJ4jDMPgy1/+Mr/5zW9WHE+lUstWPoDL5SISibwgLH1VzVIuj/zO5z9aqjFbtxZoE82F2rTatPSb7p1Go4GrXmOq5eQTzpKlr82VkXUDV4cfZ4t3haW/tIgbiURwOBwEOrvpzySW35+fn0dNVrjDd5Df3PZz1h2zcuEEWtv4lzVhHIZKvGM998QuRBMeKtU6kfYOPIqfhUXr85f8+ksLxPVmrvu/OOcvAPjoeR9FEQpGWUVLWOeU758FXeI/O06l28+28gmKSjvSE8DIZvE0k7fVyhoE3QzWJB5N0nAJ3nCghNIMNV0tbNG3sXmOyOfzNBoNRkZWimg6nSYej6841traukL0VVWlVDpz+WlOh/n569l1/w72PPxGKpUnlg88HW5K5nA2NWxJ9FPNbJdL7p0l8Z6LWvcgm82iLVbBIcC0rF5XZwBHzIuWq3PfffcxNTVFoVAATj4ZVdralwUt0NnF6MwM04lZ5utz7Pvxtxm421rcfdO6If60xWrXG+vii+s/wlcu+jxSSiIdMTp8/UyOTiMly379Q03RV6VC0BXl3ZvfzT1/dA+v7ns1AI0x6xo8G1rABHd/GHdfCPXCDrZWRskra5Fly43n6unB0Ey0uoGvK4DXhFDDpKVssLNv9SXZFn0bm+eIJRFfWFigXC4DcPz4cWq12gpLH6wkXUvunX379vHZz36WL37xi89pRE+x+Ojy61pt5hmf3zBNfrqQ48rWCBGn4ykt/SXRL4ZbkC4X2cU0sqbjWRtll3OYEce8ZenHvBSNCvfeey/f+ta3ljexLeW5mQxZic8aThd3+2I0ikX2VEbwJGeQp2zeesuGIahYAqwE42zuGuTbmrWhKtzdQpd/LbVqhYV6cFn0j1dPhor2x87CoTiI+09O1PUTeYTXSeSKfhAQuszqr+RVWVedoRHdjFmxvk9XTw/1inUvgr1WIZZgTRIvmTg2nKzlu1rYom9j8xxxquU+MTHBsWPH+OEPf0gwGGTDhg0r2sZiMer1OpVKhXvuuQchBI1G4zndtNVQUzgczXTBqiWSRd1YFu2n445UgYymc01PK10e10nR13TcQhBu5qxZstgH4q1UfUHSC9Y1KhtCHHfMc9A1hfA5cbR4KQpLFNvb25mfnycQCGDW85z41jsYNqqoDidaOMrbdu6g7nSRNBZxlfI4egdp7evH4XLR2tICleZ99Lfxd4NdbHFYTxRJj5ehC3ciEIyX26FkuYumaidFvzW4dsV1SilpnMjjXRvB3Rei6x8uxLfFmoCMhSMoSLwXX4q2YMX9u3t7SGSTLAancHX4STdd+LpQKXrSp3Vvnw226NvYrDL5fJ5du3aRyWRwuVx4vV7GxsaYnp7G4XDw0Y9+dEWhDWC5xN6BAweoVCpcfPHFAM9pGKfaSBIKbrZeN0X//zo6xR8/enqunh8msvR73byqJUSXx7W8kJtSddrczuU0Cfl8HofDwabWFlIeP9lUBkfETaFdAwEFrPBVV9xHvin611xzDa9//eu55JJLOLz7u6yfvIOt6X08NLSVznPO5/wUPLBuO4661b7m9NB2wcWIfivB2rLoB+IM+T38ccjaM5B2eeh+z3nE2wcZL7cii9b9Tp4y0QV9vSuuU0/XMAoNPOstN5Mj6F5+z7l4GABfzzloc/MogQBKJMI3R77OLVu+gCvsYM7tRGKSCo6Trtmib2PzokZKyc9//nPuvvtujhw5QiwWo7+/n5mZGZLJJG1tbbhcriect+TueeCBB3C5XFx44YW4XK7nVPQbahK8A/xKeRvlRpZkQ+OeTJGjlTrJp9g9eyrHKjVe2RJEEYIuj4uFU9w7bS4nExMTfOUrXyGRSBCJRNgU9JP1BigaVQKv7SWRsiJnhBAcPnzYsvQdNbwON4FAgIsuuoiLLroI54k7AfhktMpw9yAbNm2iZabCbEs74fXWE5TqdHMisUjO5bdCZKtNcQ003WrFApriYNZhCfbAlnNJ1r2UEnMUdYOKYS6vTXg9HSvv06jlnvKua3nCPfCnj1BwBIm0DqDNzuLq6UEIwUjxOLpDY8GcYyZXp+5bQPHnbdG3sXmx89hjjzE5OQlApVIhFovR29tLJpNhbm5uOSb/8bS2tnLxxRdTq9XYsGEDHo+Hjo6O50z0pTRR1TQP6tv4lnwPPy3EuTmVZ8kz/lCh/FvPb5gmi6pOj8cS0S6Pi6Sqc8v1R9iVLbLB6+LWW29lYWGBiYkJotEomwJessEwEkmlV2Fubo5oNMrQ0BAjIyMIRVBw14k0XU4AiUKGLWkrKsdMW08gQz430xPHePfuO6klZvGGIkina9mNNDExYfn0PWES9SyJcoJCNkvVH2SyGZq5dqdVK3dyOsnU7u/iMRvEnZa173CeLHQOUB/J4Wjx4Gh9YgqFUG6MseAALoeCNjeHq7cXU5pM1scBOJ4dwTRA9eRwSZNUbfXdd7bo29isIkePHiUajTI4OAhYbpuenh7AKrT9VKIvhOCKK67ggx/8IG9605sA6OzsZGFhYXln62qiaVmk1JkwLKv2+9XtfH0mxeaAF79D4aF85beev2TV93hdmHWdtmQDCXygVaPPVPjD0iKZTAa325oUIpEIGwNe0s3sl4upRebn55fTE6dSKVRVpUCFSLM2LcC+A7fgljqGN4ozZwlpnymYbizgkBIxPU7rmgHAuqd+v9+ahCtpGv4YV/7sSq6+9WoymQwyHGGquYGs86xNBJyCibyb7Xd9lDv2f5hN6gRIHUMJLX9+9VCK+nAW31nxZXfVqbQUxkkF+pj7679BbVr6M6UZGtIKPT2ePQaAKTR27N7F5V94+Jl8Tb8Ttujb2Kwi2WyW9vZ2Nm3aBFii393dvfz+U4n+Et3d3QQCVrKwzs5OGo3GcrTLatJoWBbnqB4mplSoSTealHxyXTc7wwF253+7pT/btJh7PW7KD83j33UyTfF1WRcL01O0trays2lRR6NRgk4HAYcfUyiMjo6Sz+fp6elZvl/T09NU9BrhhhezoVMxDFxHb6TgieHY+jZ+5t9OzKngmq+SUHKYUuIoF2np6Vv+jPXr1zMxMcH9s4JvNWva5ho5crkcvmgLE80F2zvyJZzxNUxVWvnnNf+NLZVx3nFkF0Fdo2hasmk2DHLXj+DuD1tRO49D1vK0NDLUZIzirbciq1XcvT0czx4HwGm6GC1aqZRdWpisO4XS3vuEfs40pyX6Qog3CCGOCyFGhRB//yTvf1wIcVQIcUgIcbcQov+U994rhDjR/HnvmRy8jc0LGdM0yWaztLa2snXrVgYHBxkaGsLr9S7H5T+d6J/Kkp9/NTdtlSsnmq6dJBI4XnfzSm+SLyp/y55XbOHVsTAXtwQ5VqmviGh5PHPLlr6bxok8a8uWY+hvhuv0VEySySQdHR1s3bp1+dqklAyVJeVAhMOHrQXQDRs20NVlFTVZOhaRfvRkje+MnuDVqQeobfkDcq1b+dTgB9mR3kPqN1+gIXQSsXYEUHdYoaGhUIiuri5qtRo/L0f5hsN6WnErbkxp0traSkrVKWs6/zQ6zw0bzkMzBd9reTUpVwueqVk2T88sRy+pMyWkahJ+bR/CuVJKv7FrnAcefQQAl9bM+OlycVOpxK+P3IeQCtuc5zGrT2EKHX/Zyw8vVfnCWbOr/iT3tKIvhHAAXwLeCGwB3imE2PK4ZgeAC6SUZwHXA//ePDcGfBK4ENgJfFII8cTVDhublyClUgld12ltbSUYDPLe976Xlhbr37+vrw+v17scY346hMNWpshisbgq463X59mz540sLNxIo5EkS4yCIdjoNQgbkzjQkVLyh50tOAR8d/6p00TMNS39TkWhMV2kU4Xdvyxx9bRGo1pffgLq6uriIx/5CJs3b8as6mwoGMwHrevs6enB4RzF6czh8PnZf/AgQgjiZpgvzySZ3Psj6g2F6VI/ifAQAMc9XcwuWi6TKbflY1/MW/dL0zTGx8eRSB6JPwII3rXpXaimiqZo9DQn4PvyZabrKvPNlAxtuSQ10c3x2QbbDu8h3ZzQ1CmrX/ea8IprT5cb/PNtw9ywaxcAoaSGe+1aIrffxlQ6zcH5g0Rr7Zy/5lyKSo6aK09NHmOyU7Bjcd2z+xJPg9Ox9HcCo1LKcSmlCvwIuOrUBlLKe6WUS7sKdgNLzyivB34lpcxKKXPAr4A3nJmh29i8sFnaXLUUfnkqr3u0UbM4AAAgAElEQVTd63jf+96Hopy+hzUUsnzJq7Uzt1qdBCSZ7P001CTTDACwOWBZyg/tvoKRE9fS5XFzRSzIDxIZPjuxwPyTVL2ab2i0upwos2XQJeHX9uEElICTbMXKUbP0lNPR0YGiKBi5Om+f1cgGrYnw7LPP5u6D/8DhsS+QC0VRpKRv0xZ8Dh//p17ij0r7OVDbwq5b7mS0bvn551wdPGSuoe4P425YfvN0qUI4HCaRSFi7odskWW+WV1W3c1b8LADqjjobOq3x3JK03Ge5mPU0NlTMkA2H0KUgUswwXKlT1g3U6SLODj+Kb2Vd25FF6/sZcMyjo9B2YhFXZydjk5NIJAuOBJ3aGs7p3w5AKjTFod6H8agSR1vXk64NnElO5z+uBzh1O95s89hT8WfAHc/kXCHEB4UQe4UQe1/qFYNsXj4sif7jY/ABAoEAnZ2dz6g/l8uFz+dbPUu/Yfnd87k9qI0UM4q1DrG16fuu12eYnf0ehw59mPMzf0dWM/js5MKTWvyzdZUer4vGWAEUQfDSHro+cSG+rW2ka5aoPt61pecadNYlZw1t4HhXPy0DIf7R/AR/m7mYEV8YE4HYfi6zvT4qAjbUZ0jUrQni0KK1xnDR+BHK+Hhkw1l0pxMYDgeqrnPuueeyY8cOOjo66Ntofa6r0sKJA5ZPveFs0Bv04xRwUzLP5oAX4fFSCEaJJR7mgVTSOqeapWHo3J7K05gu4VkT5t7jSY7On/xORhYs0d+gJJjyduOcncXZ1cno6ChGi4HqUOmpDnDsa9aklAiNc6RngYDqYLhv6tl+jU/L6Yj+k007T+p0EkK8G7gA+MwzOVdK+TUp5QVSygsen4PExubFSjabxel0LlvoZ4JQKLRqln6jbu0+baiL5PK7mRQbGfJ5iPmsScvpDON0Bkmlf8VFYYUvy/cz4DY4Vqk/oa+5ukavx406XcTVHUDxOHGE3Sg+J1mtiMPhIBaLYTYM0t8+gpaqLmfQfPtQL/duOJe9xQQZEeeYHOTRvnVcf8FrGHZ4ONrpwWnq+PMzLBastYLEvFX7tj+zQDYaIpBJMpSYxHB5QQgGBwd585vfzIc//GE8oeaTSd3H/AlroqspNR46NkJnZhHFsHL9101JrTVGILOI3oxiQpqsz+T4j6NzfGyTi/sVnff/1yP87c8OLl/7SLJMKOJhUJthXOnGSKWR7R3MzMzAGqtNx8JGjKyTSK2dY/G96A5JazHAupGTG7tWi9MR/Vmg75S/e4EnVAwWQlwO/APwVill45mca2PzUiSTyRCLxZ6RC+fpCIfDq2jpJxDN/PKVygkmxFrOCftxuy3LuLPzKras/xwbB/4X55z9TcIUGXLmOVqurehHSslcQ6Xb40KdK+PuORlXL3xOcpSJt8VRFAV1skB9OEtjNI+RbyA8DtZELFfNQ80IISFNpMPJhu4uDpVqHA4rbCrP81OiGM2Sg+r8HMI08asNZoIdbFqYQtFVlGa6Zqb3WH0JQboygyIFHsODq2FtjFPdKo/dcxdveewh3pyZYXfBWuSVUY1oxUWfYzOiaa9ePp1iTDHZ1e7kbxJJPuX5Hucs/IzJtHXOyEKJ4FofSraLibSVRjkdDmGaJrPMEqrHCNXbQEBHuZ+Gs45iKgxN+/FOVFcUeV8NTue/8RFgvRBiUAjhBt4B3HxqAyHEucBXsQQ/ecpbdwJXCiFamgu4VzaP2di85Mnlck/qz382rLalHwxu4nr9Y+z2/Q1Jw8fZIR9ebzcbN36KwYH/hnJfJ+5fbsbpDOH1dNMnppmqq1R0Y7mfpR2snYZA1g3cPSefdBS/k4xSpr3VeqJX5yxhNwoqeq6OI+qh2+vGJQR7q5b4+6hiINkW9DFcqXHQaXJZZoqDqrUo7nOG8edTxFQdgcSrNfBrDYSmYrqsSlSp8UPLY1gsJ4jpAoHAKZ04TAeemAejZE2mg+l5tGYEzbxnAcUUTI9OsCZguaVev9HLr85eS0xRcAfL/Im4g7f7H+TWQ/NIKTmeLBH2zPFQ6X00iq/BFE5STiea0DhaHqansAFDaSCjWdpLVqBjS6OFSMVJW1/vGTUSnoyn7V1KqQN/iSXWw8BPpJRHhBDXCiHe2mz2GSAI/FQI8agQ4ubmuVngU1gTxyPAtc1jNjYvecrl8hl17YBl6ZfLZQzDePrGp0mtNks6fS/1RgKHs5vIw0Wyvy4QrZQ4J+RHCEFvz7twu1tRJ4voGcsNEwhuoFs/AsDxU1w8C0tZNEvWb9cpln6VBjWh0h59nOgXG+jJKq52Pw4h6PW6mDAst5JL6Gwpj/Gqw5/Hlf4vRvQy5xemoeyn7NVpdHbQkk/T57Qs5MFSAlURKIZOxR/EIQxm8ifTRkyXU2BYk7FA4DW9jHgkqtdPpneQRipJS6NGd7WIIRWcnVEMXacjIlGcCsP7HmF7LESnLrhC7ENBIgwHD+9/iMVig4ICm0qTlIwOxtqO8Ok/bmGqWmC2a5aaWWXr4iXIYImcY5SWhvX/EWmE8TecHK/5z9j3+lQ4n74JSClvB25/3LH/ecrry3/Lud8Evvm7DtDG5sWIruvUajWCweDTN34GLIVtlkql5Tzyz5bJqeuYn/8piuIib1yGV2/g1jVec3w/297wyuV2ZlXDyDfAIax0wIENtGdvB97NcKXOeZEAUjcZf8Ty4LZmrbaujpNClqpZNl9HyBJdrSn6eq6Bnq3jP7cdKQ06lRITeHBiouPhH8euo6oN42tvo+E7n+3lGR6quSkENabbDLbMllirWe6VonOYY9ETvJEOHty4nZ21FKNF0yqvaJjMqkWCujXpBINBFCVC0izzzQuv5D1BF8xOcNXkEWpajZbydnb8xRXE84Lb7rgRLTvN4tQEi4uLyEydN2etsMzj5lr6KxNcv28KGXSyKZPBQLKv507y/hwz9RsoeHOsS59LvNLH3oGfMtZ6hMvmLuMNR9eRD/mAIkro5Ma91cLekWtjswpUKpYABb1ezFrtaVqfPqsRtmlVxjIxzQYLGWtSmYj3EK8U8J4SiqEtVMiJMgtmDtkwCAQ30ibn8CswXLGusXxohslDVqK02HwNV1dgxcalZMkS/bivBaOsWpMIzYLnElxdAVLpu/CV7wOg0yXprSzwqvw+Fpr+ea+Zo0XM46+6KAY0kk7Lo9w+PgzAkcAcroY18KqnysH4Oqqmi0QiwQ2LWQqigV/34FBCuHwx0oEeFMPKy7Ohs50dO3YQyizS0oy+UnIOfN1ryMsAnf4qDrXO/Q88QHV8mkvy+5mIrKVEEIeUfHNsDF/MS1euQdafIO9P0pPvJ+fOsak8yDsW3gbAXHiMnDvHgneGwcJaFM1aXF4/sOlMfa1PiS36NjarwFKRFP/11zPxh390xnZZLln6IyMjyxPLs0FKycx0nuHhS0mn+8ikJWW3l9ecvR3FNFfk71cTFR50HucX7gPkFzMEAxtQkAy5VYbLlnunfGySlMeSlchYEe+GlXsxk/kUIdOHS3MsW/murgBGSWU0IDgecVCrTRPHEvKrU/fw5eFrAVhwNnfW1qZZ0Mdw6wqFgE4mMofpdOHfuwvT0Mi687TWrK1C/mCZ4fgAIBkeHuZIbgFTSFpMJ46qi8VSAemM4jEtf/2GgJcLLriASy+9dHnMo+MTDA8PowjY6JpE6BpH9j3MTnUPGE6KPQFKeQ3PwjRRf4NQzEuo7GK8dR/ChD/eO8gH9nyWD419hEYlSliBgseaZBaUA5RiIRyG5Qrbuu6J6RzONLbo29isAkuiL/bvRx0bQ52YPCP9RqNRnE4nu3bt4rrrrrMyRj4L6vV5JqfWk04NMHz01ZSmMyxEWnnl0AAAicTJmrO12SJJpYguTH7163vw+61iIoPOLMPFKsX7ZjAmTZJeCGsSrwmBnV0rPm8hnaRVBjFrOo1xK4bfu6UVDMnnN3u5ZmqOQm2ROIsgJX955HOE9Qo/3vBOEg4HHVkPO7O7GDMst1kp3EHJkye3phtRq+BMjmEKk9ZsmKrPpCuSp+FyoXgN7r//fooPWCUT44YHxfSAVqM72IthVnljTOGCsJ/vfOc7PHbkKBKoO11MjI1z5MgRBuMBerzW5CDqdS6XJ/h26hscPPz7GLkKrkKawYUy778tz0TlEqZaH2Nw3kVvzNqEtc9MUjIlEU+dqrNKWA0x2WFy49AdGGoZzWHyxan/91l9n6eDLfo2NqtAuVzGW6sh5yz/duXBB89Iv16vl1f+6Qd45zXvxe12c+uttz6r/lKpxygW2jn33Db6B6ogJYuRVtZ1tuN2u1eIfmJuHkOYtJgBhieOo6ombnc7a8QcWdNk/O4pKDqZiyWJ1028W2I4o57l8wuFArl8jriMIIuL1I/O4+4P4Wq3onSKTkFS1bmjGKKdJG1aDp9e4ct9V+M5/43UCmHeuLuTYKbKSPgCAK7ofgVI2NtfZLJfIZAvs3UiRFcqT3lNgFJtkqBRJdkXYs2ObqbN+wGI1/wohge3oZLUrLWRj3VLHLpGpVIhnc1S9vjw6hqGpqFPxVnbtZF2bxmQOOpVlOIWVOmjmNyCo15DmCbb57MIBAWHQtq3yDkTJp2+XhyKgVNtAQTVoJUe+xWZfq5+sBMhBd6aSdmn0+p+4ka+M40t+jY2q0C5XCbedI0Ij+d3Fv3Hu4WSDY13HU/wa1eArVu3ksvlnnEkj65XOHjog4yPf57Dh60cNDt2vIn3XvNvlC55HdmB9TgVhc7OzmXRn5+bZzJvlfvbalhbb7LZLD5vDz2mlcd+NKRQbnuUxUCdsHsCx6UrE7IdP25llxxwd+Ac+zZaysQ7FEQJWRuSQppEAD+pbKWbWS6sHQBgwttDpz+IWbEmB6Psx2x4MYQke6zAuYWtJHyPct+WCWbiVXYci+HSdVq3rGO2OI5Xr/CYK8X/yXyJRV+KeC1ORzHOfNRKhOapWr+nClPLGUxNTSUXsMbl0AP4al1UM324FZMWdx1Hrc5M+SwC5k2Y8gRgfQdm1UfQkWQ+auX/6VO7iRHCcFRxmNYEmPRb93HA2EhH6DVcPPdaIuUAJb9Op/LMdmn/Ltiib2OzCjQmp1gzn0AJBAj/3luo7t6NVJ+Yo+apUE2TPzs8wYZdj3Hd9MmtL0spi4+W69aOVtNcLg5yulQqx0mn72Zi8gucGJ3C56vS1TWIoijMtHXR4bPEqauri4WFBbLZLF/7+tc4oIzT4g/TYVqWcSaTwevro7NhhW1ObQ6TPPt75IgRdk+RlysnumPHjtHa2krMF0UvWAut3tDM8r799obk9ztamJNtZGnlr+tfAmDC10t6+vN4K82nhlKI5Hyasl/nbG2IaxMfIWj4GCwN8tgmnYZbYDhdbD73FWimhldPkG3sptfXzxbHNbxnYQh3o52xLstF9NpsCKTg1omj5JqiL4CGy3LxOHUr+mjsUI4SQXwuH85KkVr+B2QKE2iFu5ev0dGQjHXA3Np7cUgHgX4rql0JWZNCxZ1hv38Ul+EirofI+yStE1NEqpJUtEGLvvr5KG3Rt7E5w5j1Oj2f+Qy9k5P4Ljif8OvfgFmtUrj1ttPu40i5zm2pAiXD5MFTctcnVCve/FiltpyxM5fLPaPxqaoVQbN586epVjro7PQvJ/lKNDQ63dYu1Z6eHjRNY//+/QAoUrB2YC17O0JIYDGdxuftIZTP09owGY7kqTuy5EULLSJPKn3P8mfWajUmJyeJx5NIX51GfRCFAubRWzGL1kTWXjf5QI81oRziHLyVKgaCOW87xfIxoiVrXLGCE29VpxqQRGUAJwqvyV3NuZlzuTT9Wjw7r+Cqj3+Cs7rOAcCh7gezQEgM0uks835+Ss2Ic9Y2a7E3OjlPUA2z8Ngwt4w8jNmsD9YwcgjAqVtPAroK45xH1lgH6Dh8Tro7/CA1lmcus0KMEYpGgpZ6C31aOwXq1JUSZXeeH5/97+yL7ieqRql076beyOKu53F293J4bZFQ7czu63gybNG3sTnD6Mkkiq6TuOACuq79FIFLLsazeTOZr34VeZqumOPNEMgtAS8T1ZNukkQzre9IpUG0KfrPNL++plmThNdzLo2Gi3Xrrlh+b1HV6PScFH2A/fv341AcvLvxKq580+v5z3U+Sl4/R+YX8Hp7cVXirCuZHDQlWVqRKLTINKXSQarVaQDuu+8+TNPE57+DzMD1NMxzCDjuRJm8j/KDCSoOWKPCgDxBl5zjEOfgrxukvFFCbhfO4GuJVFzoThN/w4m/JlhsM/G4rEmi2LITgeDSSy/lQ+//Uzaev5O+QB89Sg/VihVLb+gxtpVH0YUfLdCLq8WKhDI9s/gND3ORYb6b+wxTQSvpWaRmJXNz6AGkO4/brfLA4l/QMKzQUaPWoFi7EIkAVxvgwJQFcrUysw6DtkYbMTPKmK6RcI6ya/AnGIrOn+0NsTO1k3wxjqNhfc+zXRpew4uWf/raw88WW/RtbM4wetOX39i6BVdHO0II2j70IdSpKcr3/ea0+hipNPAogstiIabrKt+ZS7PzoaPMNN07NdOk4PbicDiesaWvadYkUShYYYJz3gB/dWyaim5Q1E26mqLvPlbHi4tqtUrcE8UX9rNX0xkNKBR8QRLpND5fH+5qJ1fNacyYIT7N/wCgw2mJ1+HDf8ni4iJ79uyhvz9DMJDDNWoJtb/tCC4xijY1R9qr0FMrsP/Ae9jOowyzlWItzpivH2/qS3zl0QMoUlBos8ZWCGgk2xS8WH7+Vt3Nu/7vj/Ka17xmeUPc8IPDvO42J+0ZB6bwM+Rp41X1UfLKOqLtAcYaBo1mmoagHkR1WgKc8lnx+d2VbnAqOHU/bofJxR4/LpxII4nha7Wie9QakY5z0Ls6QAlgqscIjx9l53CUsqPElzq+zw3x73PH4M+ZajnCW/b0E24N4zW8lErtRMnhUjyMhBdYW+/jiNOO07exedGxJPrujo7lY6HXvgYlEKB8772n1cdItc5an4f1fi+alHxzLs10XV1OQma1adDS0kJxeprZj34M/TTFX9WyKIqHdNrKNXO/6eL7iSz/NmEt2vY3ffrqeIG4YVm7cRlmb7+Pjx+fJmxAtwiilIp8OhGl3OjnikKDd4ifkSPGOyKLfOgV/xtF8VEqD7Nv381IKenqvpt1458luHA5AcdduF71XoQwcbvuZNYnaK/rSKlyIQ9hSAfttTy/8reilvYQK1tjaoQ7mI3X2L01S7vaQatqWd0bG7C+Jboib83I7gMoEvoWfWie9XT7PKwtjrLYGMTs9HK0XEMEAiiKQlBr7pyWkPNkEULgwEG8N47D8BHBg99h8iq/DmaOUqQP0+PDYc7giHTg87XhcPrBtPZObJ4K488WkLPjrH8sS1++g7fPXkFLTic3ZRV3qSsCxUzSU9JIM8/6Rh+OBTDN57lylo2NzVOj53JPiLCpzVthmt6ukzHqwu0mcPHFlO+777Q2ao1U6mwIeBloCvBS+uJDpRpbApZoHK/UaWlpwbPnYUp33kn14Ud+a5+HSlV+nMiiqTlcrhipVAq3282UYlnPX59NM+Bz84Y2y+2hLVRoN63XLVU/f9Vl+bo/n3Oxo+bDY+j8ZLbEXYHNNKJT/J75A77Bu/n77gY+d5ho5HzAZHb2OF5vhfM3XodjrA0Z30XU+UXYchVGx8X4nLdgKnniqgePp4dNDHNb7veJGBXucafB0cbv1y8CF7gdLdy1I0k6JjACb8TbTEi5viZXFB8xpCQxbkUVdWdCSO/ZTOcKCL3GiD7EX3VrVknHmIdIZIb1ipu41snawjrKrhKH16xh35oN9PdtAEA6avzc/QgHzEOYQmEx1o/hD6FpixQcVXy4ibqtCTIR11mMqVxwvIW18wG8moNXHmknttgMf63qCE3l7tBGQhM6W0ZPcPFhlfMOF/jDhYdRlOe/iIqNjc2TYOTzjL72deR//OMVx0vT05hC0DowsOJ48LLL0JNJGsPDv7XfimEwU1fZEPAy5D8Z5x4tFvjYD/+TLQ4Y8nn4xmwKPRAifMIqBKLNzjxVlwB8bSbFx49Pk25UcbtiJJNJ4vE40w0NT1NoPjHUhVtRMFUDPVtnjdlGxBOk6olRFPB3g11c5PLQ2axU1V8tkaGdfNTymwvA4bDea+94CwC5vEFLi4tAfjMAgfBhNLeg7vSivO7jBGWGN2dvwtVwY6h1elJwzuECqfaN5Mjx+ux2EkeP4lvfgQcvr2+8jcSa/2AxvhGAOZ8gXjJWTKY/GE1SL1ihkbGigw65lqTTupd39W7GEHDPjo3sjPyAbdvv4ZVbH+DyxVfTU7Ny3xzt6Wdv/0Z+PG89AdTcBcaDCv9+0Tb+vw9dyy8uOo9GMIIqJLXkCO56jRaXJfonugsc2FjCqQukolCLhPEViqi5xnIxEWc5jSvawkDCetraOCcZODJK6+E9v/U7PBPYom9j8ztSO3wEWatR/MXKbOG1uXnqXi8dj6uMFbzsVQCUd93/W/sdq1ricM6+h6m+42o+fd2/Mzg3zVUP3stVv7mLbWPH+ca2AdyKwi9LDdoWrVw36sxvF/3ZugqGwa5EGw5njKnEAkRbSDQ0PtLXzo/OHuKtccvfri9WQYJ0hTnW/2oeGrIWjV8ZDaIEXLTXgzgVB0OLCyR9Drxnnaz1q2lWCGlb62WYpkKtGqKrJULjhi8gnCah6mHmfG2svX+Ys+e9vGvbp0k1vSttMyobh9OMtF7E5/2vA6DlUALD4yNp9gICZeByfE4/a5qF2fe0OnFqJmb55CLoscNJpJHC0dYNSALpHAvuOA3p5/Z1Q1wZDDLkFHi9SSCAw2HgdKVoabSAFBT+f/bOOzyTqzz7v5l5ey/Sq95W2t77ui/2et1wCWBwCQRwIMRAICSBgGkJBkIgEEz5CAZsjMG4Li7rvm7be5dWWkmr3t7ey5Tz/THyLsZrxyRwJR+f7uvSJe3onNG8M7P3ec5T7kdxI2SFKVVHU0o8WvsETy5aTcLrZ07fISpWhYn6ufyf932GQ02zSU0cAYePgktmOJJnIpijv8NGsX4WyB5eOOcKJE1DAjPwm87z3oMvE8qX0C0yy/oE9nQcyRD/843RZzCDPzWMpopc+K8vcnTk98tv/12Ujpv56YV9+9B/SwCtMjVJyeV6XdNzS1UVlro6yn29b3rek/kSkUSMui98FlEqseBUL9+64+tcdWAXAPXxKAs8Tj7cWI00OoEsBIbNhjo88qbnHS2rzJkYRt0DLx2fjSiX2GI1UwQ7XHbWh3ynXSTquOmbfq7ByqN1Fn5WK9PhshNKVrA1eHCEPdSpAWri40TDNrBqKIoH2RBoSbMIy26PUC43AjLNNomK2o7NOIo1OcivGzbilkq0lw+w8OCLFEMmFc3qc3HI0cF98XUcy3ZiMSxYywLDZnbAEsDTdj/rQz7apoPau8OmX/9nh4cxhKB37y5sL9wLaAyvugBJkvBHk3S72nniop9TtFv5UHsNk5NdWK0VXE5zMXa5U/iNBjxaC5ps7gqSAUHM38PJ4BQ5p4+1B18hNPkLJCHY3jGfksPF9tWXELPJxO0VnjhvEtUq+MDw9TRYl6N7Awy1LmP/0vOIhcxmNJIwWNp3ivXPbiLpsnN0SRuuV0s4mhz/K3rkzmAG/09j28kYqcKZwqjfHBxlKFHgN4dGyZRUcmXtv3Te0vHjYLWCpjH++S+Q/PWvzV8kkohA4KzNMGytLVQG3rwP6qlihbaxETAM6r56O4e+8M+EMimqh815VTGzWGtNwM38gT40i4VYU9ObWvq6EIyXK0RyZrA326dSsNp5xWtKDDc7XtumT53II9lkDk9nywhgVUli8o4DpDf3U/PJFSxYtwS7WqBQyZJOH6AmpXDR9jjND/4rnDKzlHR9EQCRwhiqmIWwn+DwgmU8Ej6XptILeA/fi6M3z+C0dpxhhNhmu45wOIxaoxIuhZE1FZvbg0UoqIrClAHr/G4CRTsFa4VFTaZ7q6cnzse7htj+0H14pswFeWugBqfPTzCboawo7K6fh1eRWRNws+3XXwOgpuYqQKG93cHHP/sBrNIsABriGkNBNwPhATSrmdPvT48zUBclmM8Q9fqxaioCiYevfC97HBMUrAWcup135S5iidpq3us6062V9gYRSLRF07RHkxypa+TlZXPpa5zu7mUV1K7Z/qbvxh8CM6Q/gz9p5Msa7/vZbm7bdIxvP9vNn/1wO48cMC3iF05MseTLz3Lznbv+S+cuHT+Od/16lGCQ7DPPEP337wKgZLMoVVVnnWNrbaUyMPCmW/iBYpmFianT4z907eW4zz0HgJzThX/KdOcsdDuZN3yKRGMTMZsNdXT0DesABlK9aALmV/Lo05Zkf30rxvTC1Oy0v2a8OpHHUuPmkEfinJjGMreDt+1JIFkUtHgJoRssON8sfqodHSRdjtHYP0nZYUFXZOg0hc0Qy5AkHd/kBCCzb+4gf1WOU5j4EZn4ZrxjZuHTq3IPnYELiCfKRESB8ewIK8IrkAydeVVzuKF8HmWb6Qfqv6ub5f2TjKsDLMrcQxG4/pTK/gN9xAb6KPoWY9RuZMpdha1sZ346B5LE07EMy30uiukUhmEukvX15+ByteKsUjEqMkIyCX7pKTN4fjKicX7WlEROuXrRFUFNJmbet8QkVx7bSdnu5LnV12LRLXSUWpCR8QsndXqAHv90mqkvSCRToH0qyZTXRW/EQyXQzLjL9Ovffu57+VD2o2/4XvyhMEP6M/iTQyxX5tR0v9LhZAFDwOaj43zvxV4ODqXoi+aZU+M5Pebwf8HNoyWTqKOjOJcuofnuuwnedCN6KkV6cBB7qYS99uwaKvbWVoxMBv1N0itPFcvMiU0i+3wo0wVYtf/8Feq+8S+4Fi/GNWkKdinCoGNkkP2ts8l6vaDraBMTZz3nthP/hiQMpFSSyToPO2YtorN5NgAOWcJVKbF161YMw0AIgTqRZ7zeQcwmsX5S4+7fXtIAACAASURBVP6Eg5VxHe96kxDVyQJ+vx9f+2wWj/aRTUXwpnP01HXwHfFBpjq3gxBkMgZOZwZpuujoTn0YVUhIeo5KJUvzlEn68XEVTVHZoVoJakVGtm9l1YkgewyzQMyddODASlgxF1OnXWIsuZWjQ89SmfQSrRiEKzo3bDctfMW+ktZF67kgpuOU3HjyWRCCKVVjpc9NbGgAZ7hMOWPFqEjEUm7ywzv46d9/GFmEQRjMm5hCMgSuYis5OYCzmGcybKYLhTPmItWcmCRQyNEx/DJ5t5+yvZn6kvnsvcJJi1bDuNeUcUh7grRlU9h0g1PVfhyo2N0tGCWzbmI4Uk3lj5y5AzOkP4M/QXzqgcPc8OOdCCEYSZgFN5IEtT4H/3jFPJpCTr7+jiWnx9f6HL/333g1A8exYAGOuXNwn2/qr0eni688TY1nnWebzuipDAycPmbk86+x/E8VyzROjWNrbT3t37U1NhC49lpCLc2oI+ZOpXLqFLZymUMt7ZysbwagcBapZcMoM1IqESjkELrOkLeOI00dJGQLHkWi2WbhwQceYMuWLYyPj/P9k+PstwkO+U23w7KkTvblYax1blzLTL/0qz7/hevORxYG0aF5GLJEn30VOcNLf94OE0dJRtO4tTi6XkVRKtGr6awJnkO1fjXLh9uw6BAPV7BUJLbI+0iWMviEigDmDXlpGiiY93NaSrnRCGNXVSpOhYKWQQnFsPkyJHQVuySh5HrRbX48apDmWg9/FtVxKG4qlSxzsiZhr/C5iA0N4AiVKCXsvPLLu0gdGcfuq1DS8hg4kLUYIn2EqsQEeUcrPW6DmmSUuGdy+gXYwbq+Y7RHR7FUyky5toMwKLmW0J4NYQiD59RDPOkYPb2bskl2quJ5VIeFuMfMcPLZvfin20qm8RC2/vd7JPxnmCH9GfxJYTRVZOvJKJOZMj2TOYaTJmnce8taHvirc/jIRe288g9vY2VLkE9umM3q1iCp4lsXQnsV5d4+AOyzTWvZ1tYKQHHvHgC8zWdvhnGa9Kf19QsHD9K97hxG/vpW1Kkp0qpGQtUJj49ha339OayNjeiJBIl7f0n8rrsAuO3Ki+mca2q2D+56bcqfEIJPd/XwnLiUJX0naBoaYshTj2U6eXCN38Olw90MT8cDhuMJvjo6xX0tVg5LGh5VsHhlLQhwr6lFCdqR7ArqRB49r+J/eIxJX4hsKUjGo5DMmbUJE0TQujZT6D5O6UiKkYKLMZcZkygll9NYbGTuaA2SAu3nm7UAh4wDVOEmOTTA5FzTwr+6x6yOdSoe8lKRuQU3gXye9Z5NKPXDBNozuIK9FKoPohkqmjaEbI0gWl5C83yRZdEckwEfJb3AtfE+zhFbWeFzEx07hiNYoZj0cvyl50kb9UgSjCx2kvb6cBdiiMIxIslhxmubiIVqkCuDSJJJ0P3+kywe6WZH5CW6gnvRxAj20gAV51LsOYMdycf44YZLeOBCs5Ns8+QE41U1yFaZSjMISUKTFJLOU0RSgrzDRkb14nX8/u/i74sZ0p/BnxQe3j/Cq0bz9t4YI8kiTqvCue1hmkLmNvtV6/mTG+Zw8bwaSqpBsfL7yROX+/uQ/f7TvntbYyNYLMjbzEBccMXys86zNjSA1Wr69XWdia98BcXtJr9rF+Nf+AIDpQq2SgXH1OTpBeI18xtNMpy8/XbSDz+C5HAwZ+E87EuWknN7yD7xOJXfUvMcKlW4d0rnhLSQ65/fzNpdu8lbHcx1TXe3mhhB7zxCZK5Z/v/SkFlY1u1TOGpozMvoBC5uoe62tbjX1SFJEtZaN+p4nlJnnKqMRsbpZlTO8LDHzdSUefNH5Qixo79BLuVBwPPjpxi29gMQy3lwl4pYsgls3gDtHVXokkDRKiyNexGGgcvRgF12MSSZbjDDZcemaDSUZJZmJpBbH8G/aBRHyEzbtLfuYah8EsNQKfut1M5+hZLYSTGymz0RHwKDxYG7+Qjf44KdBxkobUeSwBu6nJVXXceDa24BIN10lFgoQvtQCqteoiSdoGK1o1osZKy7sGDuOFS5xLhrnKgzSn9gEEmAo3gYzTaLAXWEX85vpWK146noWHSNVccPMlFdy7YPfZjeVTUIJCZrmtjj2U1Dyk68ugqBjNMdn0nZnMEMfh/85uAo58wK01blZntvjOFEgcag8w3T4EJuM8iWKPx+Flaltw/7rFmnzytZrdgaG5GLRXLBII7Gs7t3JIsFW1MTlYEBslu2UO7souYLn6fq1lvJv/wK43v20RA1/fL2s5C+bVoETXa7Cdx4A8GbbkKyWFgc8PLwhisITUzys69/g7FolKe7e9mXNt0FTfFJWsZGUQyD2SODXFltNuuwHztIdXU1z3Qso6xY2Dduui9GXTInJJ2FqoTssKB4bac/q7XOjTqRp3A4isOAitXFCW8P/273MyyN4/f7iYswyUQFuVwi4imiGhpTSVN8reCoJpCMIutlUo4VfDJ3LfGABWu2RKw4jJAtXFKaj2Jzoqt5hCQz1v4w/ev/lljDdq7X9oMkcFaVTpO+M3KczvJhLJKVi3xzCIfMwqxk+1b6wn6sHhUl0I0Fnet3fJ/G+hESqRC+ddfT8e730U0tT4krSLsvxFBszO4/RMkq0aAOsnZoL6Hxf2B2LsuS0pk2ipP1ZizIW/EiJKjKnARJ5mRoFgcWrWN2ukxZkbGrFUKZDGWLwl1N59DdUctYbRO+fIp+xwhVWRc5by3CoVAbWjGTsjmDGbxVjCQL9MfyXLqghvM6wuzqj3Mqlqcx6HzDOUGXmaqYzP9+pF/u78fWPus1x161zLNz5rzp3FczeMonukGW8V56KaGbb0IJhaj73Kf55//4DnDGdfTbsLa0gNVK6P3vx/rRCyjfaO40lnpd/Orit5NzuWndvpU7f3wnO++7lzuO92JD5YITB/FM99Rd2NfDjfURgpKBL5vG1TqL3bkSOYcLd6lAtWpampoEi222112Dc0EYUdYp96bALbDJbrLWLAv7fYR6+2ha2IAhZI6ps5CEwTxPlGpHE9pEFkVXGA8G8SanEEj89LK1ZPUA0ZCbcAqmSsPgqWFWpZa8w8CilrEGDeSmrejCSnzhnXgazWI4xWZgc2vkJ1woljK4e9i+IkPv7E0ABAc3UnaeZDmTBGefCdYvrjqMK1xCHlvOpp4CnzphLkb3yn/JTvtf4ChPsL/tOHOb1/PNob+hMbWLcLHCR6P/yLVpUx/fkD3ktWHSVZ+k5JiNRQQpiR6sapajC9aiKwojHgdVZZ28w8XJ5jbz3sdS/Cr8AUZrW/BmUyzs9xFOF4gHPagLAtxpnz9j6c9gBm8VO3pN/+/5s6u4dEEt+YrOyancabfO2RCa7o4U/z1IX0sm0RMJ7LPaX3P8VdI3li190/m21lYqg4NUBk5hra9HttmQ3W6afvgD+hcsIVNVTcN3vn1W0rcEg7Q/uZmqj97K4NBPOHnydqLR51nqc1Gx2di5aBm+ZBpRKZta8OMj+ESaWaMmsRmSzLqBkxx4/llWpKPICH5RNmkg63DhKxV4f+8ZKeelAc/rrqHSqpC6yIJklTHOnSRSkWkYl1l9Ikgwa+Xf+r5J1pKlr2xmsdhcCpP1EkpJ55J9ddgrMazZJFKVn46kynX7tpH1BbDqMjk1gd/VgI5O0lkGQ6VmWRQDha+r32KLfgmGNY8+dubeZ/rM4LJSXaQrMoUt3EcmXYOl/h0A3FQaITArA7E6ikk7wfYsmmEho93AA17Yk8pjV+OsK98Pkkx1agdfT3yUGms9D4WfZdw+QZWoISXlqcsLhGRFyAEGQu+i4lpJIrCMyw4Y5B11WHWIhWqomxygYJV43zNPEMimyTnsSEIQdwRI28I0FRUKYQcbpqzYyyX6a90YVXZWJrUZS38GM3ir2NYbo9prZ3bEwwUdVbRVmemAb2rpu39/S7/Sb/qm7b9j6dsvvICxujocy5a96XxbawuiUiG/ew+2ljPBWsfSpXzxL/+GF7/6TXxXXPHG85uakGSZQsEMJned+Bz1VsF760IcnzWHYDaDtWjmmLfEJ1DKOtUxM69839IVzD15gn1799JxbD8Ap9x+QhYFzeKkJl/gvXYXDYoFjyporz3T1OPb+7/Nk/1P8u193+amyb/C8ukOCvWHqVJjtEyeWVhdJUGiqogxrf1/99KLuWfuVvbPzRDKKFy15QGUcpF5K87l1qnn+Vh6NVb3mfvQbmngkLubos0ULfA3ptnDavptNbw4Vmbf/sthz8UYukmOLeJmDF3BO99D0GJQY1eJxutJ2K0oogq9uhdnuExsUKYwYWZqqVMr+fqCIPMzBp/bu5fqsc8yJ/MUPxQfIFh8lho1zA9rHuDuyGOcdA6h58L0Z6CmJOhweJhXcxEF7wYQGoZ1Hk2+GCXvBoo2N0gSnrIZI1q16xnetm8nR2bP55yeQbY12AmWDa7IRoguj7JUNmMoB2bPA0niwtjUjKU/gxm8FQgh2NEX4/yOKiRJQpYl3rvOJJKm4Btb+uFp0j84lORjvzpAsaLzWN9j9CR7zjpeSyZJbTLdB7b211r6pVmz2HrRhQQjkTe91nS96e/X4/HTpP9CPMPedJ5oRWOl3/2ffl5VTVOpxPD7V6GqcTKZQ6wJeDg+y9wdRGKmvHNjcorwRIa68XHyYRvbFizFmcvizueR1ApZu5OizcG1NQFadCcaGs6NjVyFjcvGVWwNJulvGdzCXcfu4vbdt7O5fzMCwdbxrXyt6wXc1ofxFiyo0zr8joqTSZeCryxQ7S4etwqQ4Gh7kgPzAwTT5o5s1sp1hEtWrCjUsYSKxcCQYJbSxlbvASyGFXuggs2p0mUs4N0nxrh0uA0jV4teNijF7Ri6BW+pBlupjrISZ6HTJNuoWm/2Gcg0U6zuRJIgNarAVCMIicDodWSsEteMqOxyPk9ZrtBvVPCT4ZKqBHlvP13O/tP3O6U18ZMLwnx3vgN74DJ2KJfjy79EJP4UFXsdXe1eKs7lXNB9lJp4lJMts2maGKUqk0LocTTFgijFCJcNaooGzRULl26Zwv2CzHhtkL7QXCypIrmj9/ynz/6/ixnSn8GfBA4MpYjlKlw450wl7I1rmvn7jXO4aG71G87zOazIEty/b5gnjoyztW+Iz2/7Al/e9i8AaPE4k1//OkbBTP0cv+3zpB96GOfy5Vjr619zrlebmbzaxvBsEELwsfwZS05vauL2vjFuOtLPew6bJLPa98aL1KvIF0z9nsaGmwCZ8dgr/LBzE6fqmyja7NREo6hOF4ph8M07vk51LMbRZXPon87nD+ZM//6kLwTA+pCPBSWzKjeVTvHxEyVuG9RR/DaihSiffOmTyMjkKjlKegm74uCf9nyHg9ksavkYnoIFw2EuEO5KkFJ+FJFLEq9qJlA80+O3e1Yzmt2JbnfirAsRzJm7pYWqj7JVIFkUZFmhxzaGL6/gbTCvc8ET+6jb9mOWpOaxKJymqGVJdUfITSwiaHiQ8yGs1jQrbAqTqkTSZiWRSGCdMj+voUN+yklV/ip2dV3OsGQGxONWgx7HMAgYVmVUzcIqt05fxwOck7Hz9v61yLqMZVkDGY+Fh5qs7LGsZ7XYyaLcj/FOmLuNPf63Yyg+LtyzjY8+8HMA6kfGeaTjQl6Zq7P0xPPsXLqKuF1mwKOQOX4voUE3+ZUy+2uqyHt8uCeSKLbAjHtnBjN4K3j88Bh2i8yG+WcalzhtCh+7eDYumwUA1VDJVDKvmSfLEkGXjZJqFu78pmsbAoOjiX1M5ifJvfgiiZ/fQ/qxxxG6TmHPHgLvfjet9/0K6Xe0daLTzVPORvpCCDo7O/n7577EYX2Ugt10M9yaE3x/aIrlXhdFw8ClyMxzv7E76lUU8qZrx+dbhs+7iHtPPkl/oYRTKZNobSMci7OlbRGeTAZXscjeVavYPvsixmvN+9Nut7NqzRq661sBWOl0MCdl3qfBB49wl17gH9d4+N7QFN3TAmpum5v3L3w/V7ZdSXPVuaBnCGs6KdWCIiQygWpAIlj0cNHuIpKk8MI5l6Mao6evO+eOoF90BaX6Nh4+cR9+vYmUnKG+KLBqCpJqMOHq4iP1Cer9UbxNOcoZK3JcRQgdb6FEyFGiqOcoDLaSGzkHBZk+kSNsMWhxVjhetDCmjjE0PMhh3RTCyyd81No6OBIZ49fel9kbMN+DZKKLtCWD3bBQ1hUeOr6AE0UZ4Rqlamod95X/DMY/S6dlOReJLSAZFCU3V/I4YYtgwp9EMgzGvFdg0TTWHdrPopOH8Ufv5ES6ijsXXUOhZx2O5BNctH8X7nKWkkXijo2X8YEvfYv0FU1EwzUgSXhTKZyh1xoSfwy8JdKXJOlySZK6JUnqlSTpH8/y+wslSTogSZImSdK7fud3uiRJh6a/HvtDXfgMZvAqNN3giSPjXDwvgtdhfcNx39jzDc6/73w+8txHKGrF08df9esDbB3ZiRAyIPjM1s/wwo5fAZB6+GHKvX0YuRz64tmky2m+secb5NUzFZS9vb3U1dXhdL6etEdGRrj3oXt5dnwTDdHNuNrMbI4rVyzm0eUdbF45m3V+NxcGPVjeoBS/Yhi8GM8ghCCf70WWbTidjeiuJTwVjaJbapDVCdx1dnyZDMWAB6dqkt5EbYSmfJxbHA9TdDgI5nK8/corcdQ30u604x7OU6W50CWFBwJxvj3PwX6PxNf6x3l+7BgA2UqWd8x+B59b+h4ikkmat5aDTE43Dvc0+XEobgIZHU9RQa5fyWg4jGSYYw3ZQ8W5CJ/XgzUYpLC/DxmFnup+XLkJHCqAIB55FrtvgpaN3fhb8sQnqnn8fDP7RmUIpySTU1MoVaOcmvUKCSXDHss4FgkU2WC0YCNKlAnXOHe6d6ALK5X8XBbUXsaozUxJ3VOn4avoBNM5kKAia1SlYUQfYUqTCdo0TooGFHQSHtNdt1Ls5TKeYJl2gDbRTcjqwiWexZXfScPUBH/9+MM4SyXSS9zcKvVR1qzYWzTQnBwTV/G3v/4u1x16CoBn111Axh5gSF9HbJrog+kYI9H+/3mfviRJCvAD4ApgAXCjJEkLfmfYEPB+4FdnOUVRCLFs+uua/+b1zmAGr8PW3hixXJmrl76xlVTWyzzZ/ySt/la2j23n0d5HT/8uNJ22KUug23vRC61o+Tb2T+4n1X8CgNLRoyTvM1/v29L38sjJR7i3616ePvU0AIVCgeHhYea8QbpmPB4nbzEXCKs+gW9WGygKH16zlLUBD7Ik8eCyDn66qO2s8zVD8JHjg9x4pJ8DmQL5Qh8u1ywkSaFf86EhIVkjVEoDTFhULLrOdzK34Cuk0GWZbG0tQhXUTHaT8flwxM3A7m2z6vlSRz3FYzEUm43eSAPe7BifaQixaZnpGnnlZOH0dbx88qc8dOCLFCyz2Girp3X8b0mpplvoIqMeh+LCla+gy4J7F/ahqCPoUoW3ZTdScZ2HYamid2QvKSPFDbHr6XT285D1FbY5X55+BgoicpLCpIfY3mbuzXyA7/nayLriaG4v6cIU/cfL5LQk/llJarxdZoaNbu7UdNVGTSpH2pWk19ePhsSvJmezoPdmsoEoxyRzAUvbXFhK43QFjwIgJJCFhbxDY0qVURSJE6KZFfJJjIANm1Hm58Zf8vfbF/Devf0kNYlpAVIWdv4f7v7KZ3jPiISMwDk3w97JZVjlCp+a9W3Ord+Lnp/P9jnLuXbTiyAESCb1fq96A89deC0Ygnp1hJxd+V/h3lkD9Aoh+oUQFeDXwLW/PUAIMSCEOAIYf4RrnMEM3hQ/2dpPjc/+GtfO72LryFayapbPrP4MS6qXcE/nPeiGGfQLThdoXTjPhmyfQC53UBz5C7655kEaUwpjrV5kr5fUr+8n65Y5YBnh7uN3A/D80POAaeULIc5K+l25Inef6CdvMcmzSILADTcQ+dTfIlnP7EyssoTyBv/hfzg8xZMx09rtK5bJ50/icpmB5KGyitUaQZV9KOoEE5iNUFa4vowvnifj9xGImAvi2Oh8sgE/DI/QNZbmPK+LS4M+Sp1x7B0B7I4mrIbO+elJlJ0P8ZO9KXKOBiQkllUvxZF8hM3yO3hWvprLykt50b8PX8GKIUkkyvUYFgVXUWM8XCIr7yAwZcZGVsZbuaPrUr6+P8NliaVszC9HFgo/qHqAObGF5BNpNKuNtkgr9kCBZJ+b1rEPMiSuoKCb0slTkUYmi4MMjo/SVt1Bz8K1PJW2stN3CCVvxm2keAM3prMUKTPlnEIxFA5WBvlU23e4I/Rroq4sAkhIbgrSCXqrzQwm2YCyDDm3IKFCTnWREj5aXFGMgI1gMcrVWoW4UU1VcQ5xTaJaynKxrYYPjprPULY4GPJEuCXzdXaOrWFRuIsO6wjzqw4jULg3cjXV6RSRVBSfSOLWs4w7vKhWGTSDiD2O/+JL3/Ad/kPhrZB+A/DbQt0j08feKhySJO2TJGmXJEnXnW2AJEkfnh6z71W/6Axm8FZwbDTN9t44HzivDZvljV/nR/seJeQIsbZuLe9f+H6Gs8PccfAOU1HSfhxH/f3k/feBULhq1pVgOBiJWqlPSRysynH0wxcB0NUgQJJIlBL4bD52je8iU8lw+PBh3G43db/VF/dVPBlNE00kSDrNtNCyUiLeWkP4llve0mfUDYN7RmOs87uRgd5sjFJpFNk1n6nCFCcSJ/CHTbKoS/eT9pjBbP2hLxEZjzPe3s6N683rLxQCSE1hRD7Ph/7tKR7++JcZ/9I3MQoajlo3/3zChtdiMHp8F+z2sSyh8Hd9DXiNMFc3LMSvaOw3TLG6eHYNL/j30JANkPH4aMl5qMglZCHoaVtDyXUu8rRrp0OtZXHOxexkkrlaAx1aHQ+EniFYqAYh8CbyOG0BWmabrqJS6SbC7lbeMZxjjq8Op9XL4eZ5CAR1rlaqWusYn3qeRU6NCWuCunwzw8MLqBm6kAUVLxvypvtueWoBhiQYt0Xpto1RthkYShBdcWBRR9FlU0vHr1ZTcGhoso6joPN8eSNas5twIYrwWnFmclwTWETByDBXbaY6NZsGm8517lO0nSig1cpopThHIu3oWNANO5JSYqwi8+SEma2VtHu4f9EFzBn4LF8e+yzzug4h6zrStBx2QNKJVJ2p+P1j4a2Q/tlMj9/H6dQshFgF3AT8uyRJ7b87QAjxYyHEKiHEqurqN860mMEMfhePHx7DpsjctLb5Dcc8N/gcLw2/xHvmvgeLbOGS5kt415x38bNjP+PerntJ257F6j/IifRe1gVv4h83XECNz05v9xBKSSXcsZB/sj3Nzo+cw/0XyIQdpoTBP6z+BzRD4xfbfkFfXx/nnXfeWRunnCqWqSoVcPrO6Ps8tecpNm3axKZNm+ju7n7Da8+nknz5W99kpKyy5OhO6u1W+jJmNsx3e3Zw85M3053opuRYRq1SZklaUHTYwaqQH9HxZ3OkOhZQun8Qr8XMCnLMNt1ZtYkRVu16hvQjv8Awshw+9AyFp/6eppETJAZPImeCjAcmOC8u2Fi4kkZGOWQsoowZ8N3plBmzRanJeTBsFeTsJMW8uRvJ+WeTD7yb5lI9l6bWYZfM4LbTULBhQUGmU1IJl8NYskms5TIhVxOlSBe5oo9fFNsoy31siBnYs1MsMSRWrliBXjuHpdVXcFgk2OByMy0hhEtXSA+vIJBZy7Dlr9mYOY+39b+HFcVWGkrVXK5eiJBM2rLYVpnfyydPs1tAVFGyG1iEYE3GwjOOt6PND/D0/A0gSVgSZZT7r+EAxxmZ2Mq87wwjl6DqazasowrZSysUK/vprm/AIpn1CcfS1fwoaicg/MjoKMLguYZVrO6fx/jjVSzu60JIMkJRwCLjVgys37vjDXsi/KHwVkh/BGj6rX83AmNv9Q8IIcamv/cDLwFnV6KawQz+CzgwlGRhgw/fGwRwS1qJf9r5TywKL+JDSz4EgCzJfHHdF1kRWcEvOn9Bb+YY75z9Tr5y3lf4j2s+Rcht4/yOajr3mdrs77r44zR6Gvle+CDDEYmvXfA1vnzOl7mk9hJsuo2nOp8iFAqxZNVqOnPF111Df7GMt5gjb80TtJvkt+PEDrq7u+np6eG+++7jxIkTr5snhODhr32RV6qbcWsV3M88QqRSZKBYIi/c7Jo8zER+gqxaYLLi55odTxNJLyBpT2F4IuRGzAyhLkNnT7qToGFW19oXJjAsVm7q24ai5sHQGO+7E+f9dyIqOWrGpkj2T/Dc2M/5sSvL/qDCpf01ZAe3s5W3gVCRjCK7raO0pxzohRw11jqOJ7ehK6Ycc/N4L4o2xQ3J9/Cp8fdRq9pRs6NEDFNR00CwOHYl9ooL++Qwut1Ju28+hdAJjk4tY8oi+A+1BnfFAlkPLYkp1sTGKQR9dNomSOadDHSvYkSVsQGOdAt13iyy4WJ8wVNEJ69j7uS52DQf50ycR92L4zini7nK9nOQtSks6pkOZl9IvISheVhQVmjXqslYg6AbdDfOJxIfQkxpHM03UZbKFCZfwpbTcByXsaRgz8a/5Eeh9/Dpths56W/CgoYDlUqpmVLZjiL8uIwCumwhZgvjzBSpqb6CtOVSFu0bQ1E1kCW+v+7DfP8d1/PHpfy3Rvp7gdmSJLVJkmQDbgDeUhaOJElBSZLs0z9XAecBnf/Vi53BDH4bFc3gyEiaFc1nz4s3dJ0nfnMnuUKajy//OFb5zMIgSRLXdVzHeH4cQxi8c/Y7ua7jOhTZJK0vvn0B8wzTarU1N3NR00VohoZDcbC2di3vnPNOUskU1aVq0v407373u/n1VIpL9na/jvhH0lksaoU0aYpaEVnIVDwVbr31Vv7u7/4Oq9VKf38/v4vY0AAn0ll6WubxgbYGqiJ+RO8hBgt2DhcaENMbbgmDuonnkUuCoH+AY6FjxEIKkgHdzW3YXSEGlShzyjXMmwea9QTjDXOZP2XuMOLeCL7jPWIUOgAAIABJREFUJ3CVSkjOIM6pApQKZNUE8c4xfu7uYufIAxy/r5HBzBwaJvrxpycRcj0X7A4jECwz5jNW7GOgyYxp+KUskqhQr7UStekMF3oobfkn9Mlj5NA4IeVZjx1HIoWsqXRXrSQQioFS4frYKh6RvAxMxzcuTV6MI/pXvLzXDMIetwxjAKlUHQNFBx7Vh66UqQ2ZvQSMsVVki34kDIzULISh4PEJ1paKOHCQ9bRiL+xFFgKEIKjrPMkN5E9+DnelljFvKwCtXcf46Kl/ZW30FWJqkPaqFABjqpdvrbiB9GFzAds0r41tw2vp9rcyaG2gLOy0OYZAWFhamU88X0WwlAQEZcXByo2XsMMzm6csNk4mwbXDbMiSc3p4b/djbxjX+UPhPyV9IYQGfAx4BugCHhBCHJck6Z8lSboGQJKk1ZIkjQDXA/8hSdLx6enzgX2SJB0GXgT+RQgxQ/oz+G8jrWp88FAfuQ4vDdVprt50NQPpgdeM6Tuwh8EHn2HJaBWra1e/7hwbWzfitDgJO8IsrFp4+niqlMLjkNnoU9ElmZQ/zIWNZvPsNn/b6YUhmUxSXawmZaRQ3SoDxTIC+M7A5OlzJVUNkctgYBBX45T0EpIk4Wpx4fP5sFgsNDQ00H/yJPnUa7tp9e7dxe7lF2KXZW70j1BadJSYuJeKepIn42bsK6B7schORPl5ItUhDi/uIBpZxuFasxvTprddxlU1bopSBYdhY3ltPYmEl1jAlFKWXCGCazdgX3IT8mV/g6VuBa5MDo8u4TcCrEntY9H+ZwEo2dzEAtW0jIxQP5UkEagC3YIkKeyd2oyMTHebqTuUdNVTcSyhqSizL2KlK70VAD0zwhEMstIrBIwKgfg4uq8Wr20FhaojoNsg04RDUvk72aAPnQ2ZdbxDXU0dFbzCbDYfxA4IYmUbnrKfXdW78Anz+ed7LkdGUL1wM1LBh0X10VQT4/PxOBfrSzBkK878HoQk4VBlHGqQ34j1CJuFp+Z+gW+2fQBKGtUc4NzW3YQdScrCjsvSCkKwPzSfLc2rmEzMQkgyvv0HMQwZeToxQJYMNtRswYKOrrcRLYYJqwlW+g8DsPl4Pf2o1GsSCjqVkoycrbBw5CCzPPteV//xh8ZbOrsQ4kkhxBwhRLsQ4qvTx74ohHhs+ue9QohGIYRbCBEWQiycPr5DCLFYCLF0+vtP/3gfZQb/P+GGw/08n82jN7o5WX6OgcwAD/U89JoxA0cOArBwKIAivf5Vd1vdfGLFJ/j48o8jSzLRQpRrNl3Nx752Hne9/G3E1GGmfBL9iRKralbhsXqYG5p7en4qZVr6AHvG9zA+rTXzRDRFd77E7X1jfLF3FFe+ky0NWzCmk9t0dPZF93HzkzcTK8bwOe1MJeN8+ie3YEwTh6ZpPH2il8Hmeby/sYrMyA/Y7heUbHH8se+Qlcq4VR/vEdW8y58ma02gHnqUV4xLyPiv5fGFGptXS/S0VbPC8iyKLLPHeoLHXo5y9NBlLKgz9YGU8GwCnhZss9bjtc3HCNSjGIJzO/tZMnCSJVWXs8hmfubJUDVIElXxIcKpKDmPn4rVhi4JzgmPEfCtwerwknV58U3EaEx24tIVCvkJgmnTSk4VJ3gBHaeylwdSj6EaJTZ6LuXDOCj6+3ClOnCrQSrVR2g3vMwSMhJgR2aOXo+n0kGbWsuUd5z+UCdFSxGXXKB/7C/oz9RhyGWSmoTbN0ld82Y+VHMT84olSrYiIV3waOQm2rIjNBa62XhEp6NrHosn1lDOSugRB6rVQ9LqR4mW6bX08UjCitcwU23z6i1cn5rPkNcUkjvmbuUHi6+j396KSy1iyAog+OK6f2V5ew+LPOPsm1qMhpWQkeL6RaZ8x27DTr+AGkOnSsojAdYdUfqPVxFtPbsk9x8SMxW5M/h/AlNllYcnEkyVVQaLZQ5mC4TLAmSdF0dMS/Q3fY+jGWY2xp7xPWzb8TgVi4Elo3Lq4P6znvfm+TfzzjnvBODuAz/mPT/t57YHDDy/2IxlYpTJkMG+sW5sio27L7+bT6z4xOm5yWSSOnsd1c5qXhl5hfGyyhKPE5ci84muIb4/NMWDE0nshb1krVl8Nh8he4iVNSsRQtCT6OEzm99Pa+e3TSvZmWT3c49SKRX5yQ++i6TprIwO8Te1Okcnd3C0oHFO40YAKq5zWRW7gJCrwGq3hg+FLR05clYvZdlPfv6f8/MNCiFtEkffZtYY+yhICey6nYwrT8gRYfTcDdjnXEVXegp12lWUc5tBWoth4M1mKNTO5lPXX8dkVR2JJtOKd+dPEUqaO43xhmYC3iX0S5+ioJxLc2aI43OW0z7YzV/uNytxnYl+AlNm8DmVOcXmKpkeayPO9Cm0UB0lexVeoOKeoC8fQVMKuKPLEAhS6EhITFJgntbIuHDQJBV5MvwKR7xmKuc5e7LY8z4enVxC1jNAWtcpS914ygUUSWe+bTeLjWF+VLuRlDtM+9AIac3KBzcLrhpowF1poSBsGBEnUilHw/ZjWHqmUJxDvJK3Yj1sZitNRX9Dqe95TvnMDK3fzLqAzbPOZdRTgyHJrIyf4HNLv0uTO4qwVLhADZFXzWyktOSjpDuQMTglCSoShJyj5IRZ4zBPmcSrFPjp0T/HMGYE12YwA340HOWjXUOs2dXJD4ZMAtG6ktiKh8mraYru9aTLCf71yMN8tW+ML217EF9OoXHDubiDIQ4+/fhrzieEoNgZpzIax8jniRaiVO65nxW9BkWfA89gDP9Ujim/xOgLD6FrGnNDc6lyntH2SSaTBANBrmy5gpdHXmYsP8V8j5MPNFRxKFvAq8goCIQxTL1Uj9fmZWXtSq5pvwaB4La1txGc7GSOZGZE15Yb+MXee3jyN5vYLcwg7OUOmfjkQzySsqFIMmtqTOJVXZdTVXLgdGZQJNjgL9HTdCbzbcRiZqg4lDzULeUy70k+Jd3FWtGM6jQFzx5elkb21pKTCnyi7rvcS55TDFOwWUj5zVz/X4XLaIrMgaUXkYrMIpCOUR/TWTyVwVXMsWPpeo43X0hnVT0aOrXxBO3WIhIQLJq+6Xy8G3/WrAw+NGcu6oowP158M9aAQSC8gEZsZB1TCEuJfUU/CfcQsrCiyyl0OYUhBB5k/DjJ6oKRyINoko4um7uixT0F3t/5FHs8ZR6puw8Dmaa9p1CnlT/nOLbSoZV4MHI13mIeLT7B3FEDGTiv6WLs+hyEImGE7SixFMmyjNVxEmm6MrbdZmZr9cTKlIaPkLG7iZSy6LKCRTeNjJLFznurnqG9ph//6FoA2mY9cvp5xKxhHui8jqCini5myrnT5LGjoDHPeYr1tj4u0Af4I7v0Z0h/Bv/7UdZ0TuZLNDqs2GWZe0ZjVCsKpckivtIRDMnJ7JYPI9vbuO/wV7n7xMM4es3A6Mb1N7L00isYPHKQxJjZUFzogsQvu4jf08nATR9i6MMf5cXd9/P27SrKpReRv3ApLeM6zrLAqrqo7uxlpKeTW5+/lV92/fL0dSWTSYLBIG/bsxBd6GSTW6i3W/lIU4SgReFjjV5ucFbIWuJ0BDoYzY2ytHopTV4zGc4nXFyQBA9FZiv9dGQ6iGjLOHiih8ZpJcpKKsnDJx+lr6ygC4On+x8DJAJlByBwOjNkMlWs86g4hSkXMFc7RUUJYEgucnqOq1f9lEcu+Df+I2Dlk63folozA99zU80M2sbxBZtRy8PcFXmMl119bFvYzvD6mxFIdNZ5QQg62+dzqDZAw8QQspBw6CrnHnyJkbpWfn1ehJ+tD/HMSi9VsWWEx2ah2x2ENYVS73OsPbAPp6qRcrn47g0fxKpWSASqaYncRBNhDAwUl/l5E5qdQVWlYE3QVzhOlahCliSc2NExaJSz3EUHAIoOsg57Qm/jgTlv4x0HUqza2cBeu8qPFq6lHDfvs1XSmbQ46PPNo2p8iuMI5o0IZF8jVmeAncjYm+0gS8jjCoYW4JLEIBcfDiMJiTmWRsKiwvbIotNW/k1D+1kQP8WiRA8Igd+aYV3kEACeyfNxZBvxN+2hxmrGab5iaySbWUiTblr2EgaduTY6XEP8+/rbuKL9EcIU8VtG/1dU5M5gBv+juOXufWwbS7HQ7eQDdS5Cox/HFd+Cy6rgVLtR7XO5pamBT5z3Q1RrM6HRp1h9rEi5xkWkpY0ll1yOYrFw6NnNAJRPpSgei+NcGUSf6qG4fw/+H21CBtpu+zKBBUuxTJtjrqKZ5vjCsc1sHd3KHfvu5Jaf72YyXSCTyVDtCFIz6mVZcR727Is4jTiff/ljPLu8it1dtzExcge6rNMUNgloQXgBzV6zpmDn7qdYnjPjADfqjxLs0Onyd5K0O1GEQW1tLdFolG2JOLMLdSwqLqI72Y0iewjnC1itZazWCvFYM1ZgrmpapLbJ50GSKHnWM+hpZm8mz+3lWp7yeMlZitQVGinrRfZWXmS/tI85ejsXTs7HFt6Ku6AyGijgdbrpn72UlN9L4/CzyIbBiqTOhkO7MGSFlJbEUipx3rHD/MuhIteNVDjQ4SAu9iDKBzEcATz4KU0eIlgwm7K8uGotFZuNja+Yz2E40sF8rRkJCdVjLtLLEocZjzbyVNWPGIz3nn4HZCQG7WOsVXQmpBKRcojGoo2wYeXueZcRdwYIpQRD8bm85NQ45G6lJj9JUbOzz27nO5EL0RUL5/bsYbH2PPOHwNKwgmGhcbjKQmZ2iMBUAilhPvi29ATNk14ePPEtTuEiLtnoDrXwi6WXADBneB/v7nmBQ9ULCIsC58md5AMKCAlHpoXxmIvxybmsbdhNfSXOLGuQHwknc7ACAq8tR9Zwc2lgOy5bEUukRMvcXbTWHsEw/rjCBjOkP4P/1djdH2drb4yiVcJeMTjXmUQx0uTT97BiboJSeZQq32Kuqg5wU309Vu9qVnYVkAUU334OkizjDgRpWbqCgUOmX79wxNSdUUd6QOiAoPnwGKPLmojdM0xtzZlSkuK0TMIrx5/DpXgpGHFeGtzN+370EkIIqsrmonBl/HwUPc4TRz7P9rHtPD/wNMdix+jNmsTlcpuuhjZ/G9WuahyKna6hg9Q7CsSDdmTgsojK8VAXm5esJXrO21i9ejWaptE2tJ4lk+cyd2Iu1Y5qrEqIcD6N7DVlHfL5AGomjOSvx1ZOM6Vtx1Luo+jdSNqzDIfIM6bJOKyf5vbhT9OW91PQ0rSOuzle2k9ayfJ23s5fDf45l1qvRvU5mVVp4OUVKwDQ1Se55Ve3s3HLT9hovwg90oqkq8T9dm4YmGTDpMa1nYMgBMdbAiixHhyyQsTRjJxP8GoF1HNrluHN57jsaBeRksGuKgUrChISFvcmZF3g7qlQjN5F4ZBBUp1AJUkeMzYwYY3TbNTRZE3xzaFP8a7MjVTJeeqEuWDct+xi7mk908DG6tZ4yuLh2I5aukqXYC+XCceGSbvLdIwLLA2r2FycRJvnpyGvcd7Rk0iAX+Sx5spgGIwwxKOYDWmQJLo97VgMlbbsBIq/CYeh4ZI13m7sYjzspJLsYEJzclvvh3hibB3XzH6S/8vee0bJVV95u88JlXNV5xzVre5WzgmJaJIAY2NwAIyzPcb2O07jNF5jz4zjMAFjG8MYY+OAiQJEEAhQzqFbUrc6qHNXd1dXzlUnvR9KF8/c63dmzYy51+suPR9PnVOrwjn77PPfv/3bn7e+QljN4BEkSotcAkVNxidkaa0ouaXqipVnZ67kwbntf7TB70/JpaB/iT9r7n99BJ/fBpLA8FicA6MlrbYkCAwL/wzAg6uvwyaJWCWRbzStpy5kY7w6S8HVhGEYzH//BzS6/cRmg6SjEYpjJf19dt8REASE8tIju3fFdrRoHiFeWv7QgXxlOTmzRrUWQA79BYJuYVPPBPZUaR1+ZOgMmgXWp5dhMdzMpkoX8eODj2NgkBNy2EU7iXwCp8lJwBpAFETKRT8ZSxIZldlKE4rVRlNsGk2uImP3sqGnm4q0E9kQCeTLsAhCqbBZiGNI9ZSlExiekq3DCddy8skW5p3ltM3MsyR6HfbkTnTRg7WocPnZX1AzN8HehuV8e0U3jVoNGTWJP22mLGPnwcqnsEpubsqsZ5F7BautmwnLcc7VNVGzMM9lfVncWY18bIahxFE6TaUnii3Hj1Ku+4nm5xgZf5zGmTHOdqygy38FN7puRddVhFwMufUK2PI5LjT0sPbcaVYIDawNKxzyCygCQJ4ppx01J7Np0VnWl13AnJUxoVNn/iwm8/0kpCS6oKKj8/n591Gh+tmU6mDckJmylHyFCiaDWdnATul3ecYS4Heygx+9/3scWbKeq44dwJSOE0gXsFYs47AzwK/aKzAcJj47rHC7WlIp9Sjpt86/f3L9ht1CgbJ89K1tq2MHMEwWNi+6ib9yJUiYBdrt4xScAu7QKiblJFvMvegRD4YqYGoI82rGxBPOc/RfdCfNa3bWmSawe0q3gdDAtfRHFlHh+LeON28Pl4L+Jf4kJBSV+YuSxT8VJyZi7B8Jc926ktXTyFicp8+eAl3mH7fdR17NYZftLA4sfusYy5k5LKrEdHmOfMpK/lw/0Z//HM/ZAQBee/ZWCskFMIuo4WHk6mbC77kKuX4DNZlShl8cy1Gs8lOwmilraCdJNeW5BqIhO9eFrqWlz8UyeZai10NDupxRf5BUtZMtyc2gBOjwdTCTLmWnhmDQ6G1kx4Ud1Lvq31qvtcZUsq5SITLrLyfmErAET2NzlfoJNk7kEV4K4bWInCg7zla1i5VGI4qhUBDqKEsnkNw5FGQShRYKiVoWpHKqoyFEowZZmaRt6C/49KM/oOfALJed+Cn3XMgzbReJORxk1VLwaSqovOE5ygPWr/PI/HdQ0ZhzJvhO7cMMVwVonxxjzbBI1FkkUuMjmLuAlLdgAJJhUMxFuZDupajnWTc6QsLt52cr65nODjEVPgKGzoyYYKB9CUWTnY1DF9BiI6yZGSRjljkYEJj0nuTDvp/yl7Yf8pGmy7A1m6i3J/C4kpjEKA5xlmHrFNXFCk46z9KdKzm52HQv/zBdiaE5QSiSUsvIL/UjdJSK4D9zV9Ac62G6spp7f/9zvvD8Tixahq5pDWHxdr7UY6HQ46dtIcbs/ABj4WdZr2lcW/zD6Ew9vgwME5eHX8eu5FibyvD+yRyFci8pMcZGc4Gb6/YQCpTW6mtCq1C8I3y58hd8turXpKYdmOunGbFHKbhHuKpYKvwGTDGOK/U81Pd+cqqFsWwlRd1C7R91vfnTcinoX+JPwmfOT3L5sfM8OhNmxcFzjGYL//lB/wn3vz6Mz25iUXMp826ymUnrM/jMtVzRuJVvbPgGn1z2SQzD4Onhpzl24hhDhw+hCwYRn0E2kiO1u+SCqZ/tRzIZJCZALNgRarNosVEEXzM/bT6HvvYOxJwBZhE9rVB+xS3MehzUNDag+QPEF+a41jyIo2ih39vPiM/EGSlOmerjkHyKiUoL3uCVCAMfp/MZJw3D3Rd9+WEuM0tey+Mxlzo45y4MY5srMG/RmHfKNCz7NnGXgJCYwmtfjD+fRX+p1C27NreYD8VupEGpotdV6nlcHnMhAF7nPEFqKUs6CCrNhCkjoMUpYsLKEhK2LGM1aarWhEg1ObhqvnST6fNJZC8OF9GzKs68RCGQ5UJ7gogcZ1m6gzF7kpTTT9XCKI0LCmM1GY41ZsDkZzJ68q3/KJyfZqo4hiGK+NQUa3oPcKitne92mvDqpUCYt9j4TYOMr6CzbS4PsQu8O/0cbkXlueYiX1nbgIRGSitjvOGr3Lzix1zePEu9L84LDjujlizD1kkaCzXEakpNXuPmkm3F2cL1AHg9vRgC6JU2orUOdJtErfsqRhq24chm2L5/D9L6T3G+zUW9cBkPrmylUOtg1dFT3LH7cUzZM6RTI6yZ/BnxxD4EBDSLnUSxE38xRld0gr87+BDXxtPM1F/PBbeG7OrHmmihOXCYySoHC4kGTPlyQuYIk50yC/4ccyfLkMxFrrnsPtb0PENz0yEAIoqPtGHmVGwpewZu5FCqAsGA1ukuFOX/e++dS1ziPyShqLweSRFVNL48NM1sQeFUMvOfH/gfMBJK8ebgAh/Z0kJQUTEJAvfd1IPFFmZpZanV/7ZFt/HBng/y0vhLfPPgN3n4tYeR0wkCra2syl2BFo2Q3v06iCLq3BwBd4LEmI+p9CCFwlFQCuyvSdEb6SPtKWVgySZABLHzGs5X+RmL7sHlcyDW1eMR89x22+2oLSozFUfxqXMA9InnOepU2YHKuvwpfNkwVwynqRtaBUCsUGpMMhulZYPTu3bSnrWgCQL7Kv1UlF9D2l/qNHUU/bx3PItZkdldc4QapYI1mW7+uv4BnijfxeXxtdwSrKDgzNMmDbOfrfjT8OOlq3GQYWVhFF9c5wO7E9gKEmcXR7C3iXRk22lOq9hUnV6vhCGUioVp1YIvYea4U+JsTYqInKSpUENNYS0A/vgsvkyOqYo0KecYqcAqdENDAMwWD6H8JEohQdFfhSBJbDizn9Wn93O6Zz0vNwc40dnDI9e/iwMVJrrOHSDut2IoGtnI1WyLxNjj9zMoLMYTe5QH/+4r3Pr6ThTRwgmnk1Z7jK+XB/jLSj9veI4hI7F2ppq/b9rFr73D/K/lFh5bvB4nOa4tWjEcMkgChsmNstTP2bpNHFi6js19pzApRe5bGuDpd3yLz9/1CX7VZkWczXLbi8/hSacpFv7QDV0sJlBsDrJmN9PWWhalh6mNL9ARm0SxlaPJVqZtLczrE4i6GSHdQ4UzTGRqW+k385zAMMA9apAL2yik3HhdJZlxVdcLOCmdBx9sf5xqxxxHU80kHUXqTAlM4gL/hxk6fzIuBf1L/I95JZJEMQy+0FTFDeWl4DWeK/4nR/3HPHsqiCjAe1bXM5orUKP18+vRb6FLUbrL2v/dvvun9wOQkCPomRTLNl5Jo6+b+tkpCkNDeN9zGwBdoxHWDcyQPvEwydN7wGTi6Y5J1jtWk3aUguDxaD+mNgfF/gQCAmm11KxkmK3ERTOLOxdxk/MmmqcCNF3U0k+Y53gymiZq6HRlRtGrbRREmcqIC1mT3/qcyXzJnmFm4By3lNuQDYOTrgpE0YK74240EZKaiVuDFkY9Yzzo+h1ZMc8bzmMcd/aDAe9cuJqOopfFnhMUDRMH9G1EXCJpk5W/KP6YQO0CywI76dx+kC94C3ytNYvbvcBad56IPkdLOEafV0IvL/nUIKv4kmYKkoEiCMzLYQRNwx8uKYzKFiJIBnQEVTImFRfjbKu6Hb9/BQ2e5WiGiiGIjDTkOec9R8BUybX7XqBufpaTXvjdVTeyv7ECT9EgJ77Ir7tKDVXZ7FnWer9Pp97LtpP3UTZ5kIaFEFccPwLAZ2qXcF+FDU0QSEsSk6YwxxigoL6DZxa9k2dWvI+D5SYu1Dmpsbq5NbsBw/2HCWiG14wnEseWz7F9XiBvMvNKvZ31c2m+fSrF2iOnMJ2LU7Cp+AvzOBL/xgLDMDCsFhaMChAENnf0kXRrhLxuVLnUbFUZcNM/nEDHoEqKki7aKQ8vo2ANUVs/xGiwEeZMCKKB1R3n/xqGZQBN/klaPOOsbjrGhupjTKQbmM7Usq7qTdLhgxhv81iSS0H/Ev9jng/FqbWY+HxTJf/a00y1xcR4/r+/vGMYBjt6Z9jUVobLbmJvNIUzu5/dk7sxMGj2/mG6lKZr7J/aC0BWLGVTLStXs7yhnubpSQB8730vlDmwj4NHDlAfS2E5OEUoEMChVNERb+B08QKvOc4ymp6h3/gFYl5AdS3jQGIFJnMYy9wkgnkWTVPIDeaYck3RlK8lIWZIiRmKowssVqPouTxnK8Lk7SbcBQV/plRv8BhmZrJRDh/ZzrNrl/NqdTctmsbeTJ4nh56ksvZOYi4zyyJ2PAoczURIiQXudb/BDyufJW/bTKL62zxf0Y/XcNDkynMqsRx5LMaRhiAYBmLORmXOQ2v3IKJmUJFXOB7yU4jXIlWfIJSZpGJ+mGGXyJs9AfzeDGfa0gg4uPPlBm7e38031l7G4UobM9W1eFMJcjJkLDJXnTbwJ0zkoucpGkVWejfQbCndfIteP+cDwwx6B2mwNFCWUVg0OcpAUyvnm9u4aUbhyyd3M+WfpsI/hOYWSCuvUCWN0nz6e3z94WN8bFcp0NWFSuZjsqmanZXbqSjaWZYvUAxfyRep4tWAG0MQcR4L4txbcsmUq5KIzs9gCkSxFArUXpzJ0Xw6yHvOTvK6s53b7/oOObOZxqOPI5z8ObbRMQTNIOPUaTo7zeV9I1gLFxMVQaCiNcQhTw/dqQt0mgZonoMLjX+YlaB56smpeU6rfZirRhgMbqBbgLQ1hFoQib3o4lSkFsmmk1HsGHrJr0kU4BPLfs7Hu/8VQYCNNUfxW6Pc0riTVepJLO4ksvSHROHt4FLQv8T/iJFsnt2RJO+s9L1VpGy0mpn8H2T6xydiTEVz3LSshtciSVKajpIbpNJeiU220RPoAeBX/b/i7pfvJqVlMCkCYUsKZ5kLb1UNy3u68UVjFGWZX5hdxP+iBvVjW3Bu/Rqh+tKErWBlJbWZWmzSaWKJGM2XdWGxCPTn0hTJ8Kp/NceKzVjdYcyxEIvM/YyOHuVc/Bxz9jnac41khQJV0+20h8bZEn6lNPM1kMDiMOFRk2iJlZh0mXXZtSwoOr+ONXOsZg2P+NsYk00k1CJ/c+hveO6VFwkV/4YvnTeYk7I8bMujSX4mPb1o5gQp110UzU080XkZaQmcmWUI+w22nfgNSXceoZBjoL8M3BoYkH80QOyXJtKHlyFObKPomiHffpQbO35NLZP8tvIuzrSt40RLgspEANEQGOpoJ2+S+X2jjbHaVmrmBshZdYJeF0vHDCSjSMqhcMB1moDhwi8HoOZqDi0KkDKlMQSDV2sO0qw56JiaJOwLkLY7WBrX+HX5Tq6LrmLBT5MzAAAgAElEQVRbs0piqYb5tMQPB61sPgiSAUvGDDQBXNk0tnyKjGMzaf8HGSu7ltMWC0piBSoST/kM7EUVJWpQKJgQEkVmq110axNY7QrtU2NcMzWFO1pkvq6OR1d38FydhVy9ByGnUjYXJKEsoOLCoaZZNB9BpFSUXjp1cYCTYdAv1hA1e7gt9Cq1Pxaw5w2iNaWgbysbJptpJmivIeJ7EkSNNVPrIaVzavwkZ9+4ClnXUAWJGaGWH+z/K4SL3cMXsiZspiJlzpKCzGtJ8J31f8OSmT6iQ14Kggnlz8BP/xKX+D/yD2NzWCWRj/8bC4Amm4Xx3H8903/xzCyPHhznOy8O4HeYqKsK8dT8AuViklhunru67uLgew9S5yqZUj09/DS9C71ImkB70EvKoSLWjDE5+RDl5eVU53IkfD7+9kKQ+8u34c2+B4D8jdcwUuHlmdpVpArVyGIpy3TIk1ym1nNEz/KQ7QTDF62Yf605oc5G8YzMnj376C3rxWUI1BUCyHmBa86pXB1+HVMxwabKW/jKwsfozrfhUZLMpxbxnoXbWBsr6ccPxXTuOPcrOqafQ9RKVgcm0c7e4WH02GKO2ub5lG8vUvN+ojX3UazswWxfhWG1IoRzKKYyTvkErBPrMAezNMazaOYm5Ow4V++bJV3RT/yCG4/RzK+ulKhK1lCxsAoMAe+Sk9QqCt/hL9mS28cTy27FEKqoWsgBEkP1JafRI2UymmRm6bk+LEWRab8LQ4AvPK0x3x7h4dZXOFW1kzExwosuD5uqX8SsGBgG9NYM4klnWRSLv/W/tiQz1CbMfFrJockCTywv/a4fedlg7YBBxFXaL2Uzk7aYqVuYo2BuBECxLiXl/hT5tYvQ/BYmAxb8UaVk8yCkkIJZZt2VPFl1IzlHM+1T49x5aBdXHI8z31jqjdDqHSgVdsRglglrC/Z8kazJSgVhmhcSGMB4wE1ZJo87W8CesPD8/A10RcZYe2aEGa+TJ9ZXogSqEM1prP5TKPkA47Y1ODuTpBKNtOfaGU2dIRKbhZkpZLuCdLUI63S+tOGHb1krDE5tRf83S35pwclnpIc44NlEPmqh3BtDfJsVPJeC/iX+24QKCs+G4txTW0a5+Q9e9U02M/NFlaz2X1ub/O7u3fzNK69xcmqepu7H+djuD3Jw6F9Yayk98i8tX4osli6YVCTBaPwCW4rd3LK3hnKhdCMwrfIxH9qJoWm4FxaIez1sD++ianojQrqkJim0rmRXx1qOmrs4ptSSjZYyuPneEzRm2lmd72QnFpyAVcwgh+o4WG8jUd6NOGvip+Nf4cGhr5MUZB6PvYmBwHjdcnZuWeBg3Rgr09145XJEdCQtx2FjEcvTi1id7qJQ3ENZ0cI3pz7Pu3q/ioFMLrWcXdHL+BUqu22/Q3OcJue6AQSJgudm8oH34dejLJJLipUphwxpNxgGOZsTXXKzZHKIenMew5ImH7NgbdnCeLUJwdNChe4nPdNDfGwjnPwIAvCRuZ8jGCrRmm9zcPVlJLyLCJW10RAqFac92TR1c1NIhkjKKXCiqYqaCNz0Uh4Dna/6XuBTi74Brf/Cxvvhy0/rmBNLKeTASASptoyCYeBUNIr6OHfkG9B9BwA46IY9SwRWXTBIOqy8vv5uko4qFsolok4TjcHZt84J1dJMwbsOwy6jrA6ATWY6YEFY7EZt8WJIAoFkmC8u+gKGIXD1mV4sUieJKiu6VaZ1fAjDLiNg0HmuH1VxMiIvY14OsHloAJFS65giixiCwdrxGR7ufDeBbJKvHf0lSZeJkWVuupaU4cpUY3LNgnEG0Zzmekcevy/B2HAAXSwSzk9f/NDgqM2xvKmPd7TtwW4ryWN1TWYlI6SmV5KcXEUk7WWCFhKyj33tK9FFE8nqIqJ0qTnrEn+mHElkMIAbyjz/bnuTrRRcJy5m+ztCMZYfOEdcUf/dfvNjSXbcf4rf9j1OLJcmYn8Ef9MTbFs1wXDqKE3+VZjTbzIdfAyTaKIr0IWh6xx+6nfsefBxdAzMZ8O4JAd1nlLgjjuqSacHyY0MQj6PEihneUrjQxdUxp0iUpmVc/OzHK1YD4ZBFBfn44souqapDV4BwObkSlJKNasRaNOPcvvIccr6/AyaG+hU6klqMY7MneLJmYcpzwwheFcQcMk0Rh08UrGDFy1HCZpLCo3LlCQDEYHvZkf5+vT7aM818PvAK8xbJqjSzIgz7yM3eQMGAucosq9ikJwzQd6xHn/8DBpmErqV7pnfMm+TMGsaE3YRh8mN7rSxECh970UTUc50lPoMCkkzr1RNo6IzW3WeoqFy5JDK5KntHMprqHkXXrmRd+/9Z1omBzm06nJ+dsf70SWZrUd3szihsW14DAOdrFllqCbLgtvBQF0Vi6dhU7+BXzJAMFg0nac8CktGDe4YmeOLv1PBMBBWz+AsTrMqqjPoGKS88iRJN+g5JzlD4OFrRO79hMTDN11JQFnL4ZV38fDlBsEyE02zpcF8K/VjGIIIhoD74BRS8eKyhwC5BhcLbVVoizwk83YwDK59Yz9LkjKW5isJlosEolH++uc/Lb3X5Cn+9vWf8eXjv2PKVUHU5mHtQqmoXDSJNKWTJOttnHc3E7F5+GD/S3jUFIcbmyhbGcXVNYiYaKTgniY1aMdV+waFZDdzZzsQ+5MMbPokUSWIqy6NZFHJBNvRig7yGT9DU2swDIhfuAy3T2Pq2EcZ338Vsy9XMnNx3HjW3kKupplw+PK33Ybh7a0YXOL/1xxNpLGJAj0u27/b3mArqSgmckU6HVbunwgxV1TYFUkSLapsC7hIqTonfjvAdKyPHaf+hb7oKKIlRAFw+8eo0Cuw1H0FSflHQpkjrKpchVkyExof5cDvH2NhUWlNYMvKrVyYVLiysJyXLMeZGhHZqr2DyPGXAFhtv4bUmA+vbvC5lTZurPfz3DM25jUX9aZDhAvLOZev5vMFlSNTv2dJ+y048uUYSKjWCaozpWJhe2aE4FyGhUAXR0LP4MsGafNuoNFaQ7Olnl9qb1IvbMQdjBM04qyhl1mgqTDOe8Jv4lUT/Kg9wJBlBi8CP/ftYj5zJ6lkJ2bPCdYn1nEMBQlQrStBkNkyN8A7BqpwGQUWp+6iN2jw991Fxh0mJEFmm+edfKeq1ARWHgkjtpTWpBdYyXOVL+DKGzxXvZPGmERWyvLbFT8kJ+d4cgFussyxsXAjta88gXzTk0xUt3ImqHG3vIV7D6eZTKc5IBpMl+fob0rSOu1gNtBEezrEx/do3LtIojNh8JEBFdUkITgMtr8aJGuBYx/QqFmk8YXU/TTYZKYXTRIP5rC4TcRSfiCMzywSd1q4fngbeSmFlUYwdzNYM0b35BiCoVPbF+J0dxwWzNizBkKySNIvIB8NI0gifk1nvsuHUlEK+geXdPPp4Gnyw88zeuVt3LR3Hw+1Xc+dzz/OttNH8RZKE82+cvyXfHbL56jLzV40lNYxZUBakeHNsm5kQcHcAIcq34XJsw5X3ddITa4D3cQe92mq5UXU905jc4Oe7kDNDRPc0wiGQPmSKLLLYPzVv2T8ta1IupOGnh2kplcSOv1ePF07+eVNKkWauPUJH8PpdnCBUymwb+kmFiQ3X1VVpItjJ98OLmX6l/hvczSRYYXbgfn/5hXSfDHTH87mOR5NMxIpafa/NzrLw0cm+NbZab6z9wLaZIZMZUlx89LE7986/uT8SbrKl3EgmmJD9ZX87vrH+dEVPwJgbqjUtDRoHcNaEKmwmKkp1lAdKaclV8uFYhD/+LXkdh0Fi5NkQMSr28lRJOCUuP/AMPOag8qyEKbaI6xKnmZa8NKbFEircQ5E93L+4pTSIf9eWnMmrJKDsfpl1KZmeX3+GXzZaWyBrVzp20SbrRlJlPHPTOOaHKNqepSnWp5ld+tFu4hYL06tlPX3Z9rJDH+VmkQZvaklBEWdqwnhr9xJ2t1LDglDdSOKTQh6jsVnTrMirLA45WHCN8yyuEBnUmTMoVPQc/hNFWTLu/AmwliLOczOCQwDTroHEQyNv93ViWgInBNPcqInhU91cfXgB2lVJJ4sZAj6c0xWZGip7OcGnuce8TyG7OCCMEaTs4etazuxr4+StmsM1adwaW4y7y9iTQh8+2Gdbz2kYz8uEW22Eb5HZeEmkc9+UuL4YglBgHb3BSyuQQKWHK+Uy8RkkZCpZGew3ixz85lPYtasvNb2EBoxuuc30V+v0n2hn3/652+SFPrY9tQuLGciKEqRjEtkxbmzSCmVtskJTEkV8+kItr45Ar0zhGoqebHa4IB5HkU2seHMKTIVXWw4d56W4B/Geps1lZ+88UOseYWCLGFWIOu0YhkSOSIvpbvsPNq1cdL+NYCD2MjVxEe3IHqmuLxunE3XH0Lo1LH4JlBjndjLc0QnLCAY2Kty9NoXM7FhiNnmvfQIAdyzd3JusiQbjg5dS9woI2V28fsbP8hwbgn2WIKe6WEGqxrQRBnT2xyVLwX9S/y3yKgaZ9M51noc/4/XfCaZLoeV3QsJXv/pWb74bJwv7Mlgmszywd0pnG/MU38qQdYsoC0vBUQNFUOz4rX4SBQTnFkYwj/+OfYPfYtbn/4YX3u2NAVr5vAZ8iaNWX+esoQFNWPCf3Hgd3O0mglLEC0vUAwO8FLNEjKKj33yAP8oD9EzOIgcVqgX41g9z7EtvIXrAF8xyjO2Ogwgm4lwQo0jYJB1DuHMyrhkH7c4r2GffwMNuSlEDK6wlmSj4VxJFhowPDhzKjeMV+LIG7zucpG1aiiCzLN112EAnqyKoTs4G7mdfKqHd4gKq40TZKQ8I57DNGYnaJyuIWOvQVKmiBcnwNBISCl+6RmhIKdpTEPUauYB129QdJVgeRUN4TCbqz+Mv6IeJSUz55pj8aRBg6mbukIlfbUp4rYc93gF3rHx13wgXkOTWeOZijdpbe3ELoJhgMVS4APtX+WH/gfpS+wm0/EafRdFWGc7EyRaXkauaOX8MqiKQ+RKjbHrNM5fFWCqTiZ/tYLLJRDMWTkysJrAuTuJTq1mV9LEyykz3521cVIt0rawirp938JbqGPY+QTT/gnm3cPUJNopWKxEnHYWjY4wK5xnxLKYztgIGY8T1Wplw/l+bprYy4d7n2VBAEc+D0GF5WOnEHMqv1xzF89tvAJnJknz1DCfySdpmhnGABRRJLbExUzt5eiCSMon0Vdbmo+g1hcxhQQqQgkEDGpsCcyaC1HOExm4gUKiHm/1mzTqCuZMkeWbT+NynyWbbmFRaxi5GXztcUbMHfzI+lUea9jM053vZsdiC59c6WPeqGbek0XQJN47dIZ7+BkxbzmRMi/ts8NYVJWiycyayd8jiJckm5f4M2R/PI1m8EeDPsA7yjyYjkRwTuXIdLuxLxR5/54UAtAzUWRRUOFYu5VzySGsqh8AWWzFbildhMlCBi3bwDLHBxBNcV6au5+R2XEetu3kucvmyFs06iKreH7Kh8WQEWwSLYU6VEEjFD2ApCm8UbOMl4CjKLyo1vObGSsFBeodMRYnK5GQWOlZx4pEHwmTlxmnH2c6wQk9RaMhcMfYSsjncZh8dOZF1jVuptF/Bcu9W3CZAsTkBG3fuI6ilmdV4Go2V9xK2dIP8Vc7ajCf/3smyq/h2artzFcVicseAsWSZ3y2WAeCRov9PMdqMnhVF18dfjc3zL/M5ecLaKYG5NwCnpptmCxefut8DsvAMUYj52jMluoiNetmOb32IUI2iW2FOqqtLvqsk2QXLCRcCr6MC1PVUtpTXu5omefeigLl5WOIch778kG2e4qETUkKljhnchLPzdRxWJxHF3Q8/izKpqcIillCGrSadQoCZFcJhNzDfPdqmUc/AYV3abyxWWJ56FOUh1ciiho1Zo1pTadsbiNlM1fyalKiN2amXNYRBIPjGRNbJt6JZE0QVh8lIZc8kcbKBxERWZTYTF95A1YFbnu5lZDNh796CLWstITYMB/kk6eew3ZxQtp7zr+OIYgY1SrS2TjhQDknO5aw/swpYhYn5ybfwKZqjJe5OVdXxmzXdobb3s2elbewr7GRsK+avCyxp3sJAJdHznB6YSkvHvkUABUrH0JXpymmnyd0bpb+p9sYfLaFbNyMvfUMGBJPmT5NfnM1ZZvmeLW4BMHQuSP5FCGxkkfarEStIk9scfH0hipmAwK1UwKrOIqsqRiiSHN0jpHKekRdp3nYhKpekmxe4s8M3TD4wdgc9VYzm3zOP7rPlV6RNUN5hmpMbL+nC+tKP6IBjiVeJAEEs8ixNolQegxBXkPX3CYMIUYwOYxdtqNl/holdCc/2f5pbmr8IJLrDB9+5SOM+mM0ZSq4d+AGZiw38Ey+nJ3SOHOWJLWbNwBQCB4nZnExUNbM4xTZqdZiQidnyIjoWCznSYgJLlT24xK9VDlKF9mIsxoDCEoOygrzNNtvp6BliXj8CMCdcYH1njUsdlYhCAJHhFHu++cfcjL9JhbJRsBacnvcWX8rISAod2K3F/ie+gAJq52yYpSPii8iGCqWslc55Jig3znIylQnwcgu8pKNqCuALtlZ219ku3IrJ2392PsnqYzIvOzciyaU/HdGi6sYs5dulq3yeb5X+Ssey6d5yGTBEEAq2hFsPlaaY7RZdapknXNZkeHHW9E1gbqCkzaLxuOOMzwWMfOGEWV3qqTAmrOq2CtyHIl4wYCPiHWUSQav5SSen2whLwv4TGvRVDNGqIdatYzmua0IAtSaNdIIPN3Tw4EABJUhcrJBlwD3VhRYlGnGorjwdO/AnYpTlAUEA4Z8fcSt81REN/BA590807KFq8YGuGfqeRYvHkZrdNIwOcXi0eOl73+xcL916iQ16QXi8QBSJI88EAfdYP/ydXjyBS6fOkTeIzLW7SJSVklmYVPpBHVuRrZZkfzriTqtnPQuZspdSbl5CdszMp2RKqyBESJzCYqp39NXYUJNyhhFEDCY31fBoXMzZKRJdnSu5sXMXfQu1DBeXE9lQuFoYRWSATeFgnzy+DgAYbeEYJlAS9VgLsLi9AUEw8Ctq0z7KtBFkbH2Gy5ZK1/iz4/nF+KcTef4Sks1lj9yguYLKe772eM4CgZam4ta2cQDMyEedeY56NTYcHMrW29rx2eLgqEQ9jazIng9ujFLznkF37r8FyRmE1hdU1z2+GY0KYxRLCMqzLNmwMfXmj/LNdL1TCkCBgIntFp+kRnkwy8uICsyzuA4x1ssqIJInpIk752uBaBku2tXJM76z1KbKT1VxNZWYJHmWbB1UHPdJ8lJNiqyF1gaKjXQHK0r56wxgWEYqKHzCCbIk2dWncc+fIaJaC+z2T72ZIf4EGle9ddTgcAAOp/Q7WzPVHOr9Ti1ZUF8MZ3bB9/AaR5i2HOMpJxhUawFoxhl3NnC640lBdH6rIJojXM4uxtzUWTX2hBTVX5kdZoWY5hn7LfxmPIBBENnvPaf2es/gl00mBFK3u9N2UoQDaobgkwURL4/6GTkFS+5jI5y3I7FleLm0yUdu4GAN2lHMQTKZZ0FVWR2h5/5BRFPxowwY+POQIGEJnBcmuemfCtrmvqJH/sIH5r6MBnLAkVzSZZYa9IpODZyuiLAw00CNTNOdBGqoxbKTQaXpXrQRYWymrPMtDfy+hX3kfLdTt6kErMuYFattKsjnK6r5XBVFzf1HiLwZoCr+w7yiScfwZWHV1bAL7fdjIRGRTbG2vRZ+oXWkk12XsPUFyNvtXJq8RLsaYX8lQr1VwYJmapI6eDzJkGwkOi+EqFhionFTs6n2phqXk3Os5hWxcBrO03DsgdITgZQMCE3Q7i6mdZ3TFO7ap5E0EVlVkdtSqFJApMeB5v7v0jY1kBZXGe0vIkPjRb5aPFxGhMRvBmNplAI/8wxBEEkNrGczdoxKhMRsnYPuijiSee5UK2jGZcy/Uv8mbFrIU6DKc8tFd4/+vrpsbMkQiVTtE+vq+f+3cNEc0VaFvnYMxymbWslfeV7Eeb+sXSAUEFv3RAIBnnHVr514JdQMCGZzrI438LOsR1UjF+NPncFHZEGGjasZhRI6eCmyITu5wWlFTsarf092ItwqiuKyTpOlbSA5hrkBdMEopwkjYWobQiAd4evIiGlOaD8GsMzQFio5OWMCdHQqU0NENVKXjl3T6ZoeuNRsm9+A7JjaLSwv3AE08IkGAaXtYRoKLufRyWDWUPnk+h8K1fEAGapZ9ryIYzrUrTfPEnTsr3cMbaL2yYcaGKR2kIFC5OlRqbrBo4xXVVqSurY9ivGtnyJNusMKbuDqKfI0uDlWMvP8p7o32PO7CfqtFIRyfDSnBuPLvGJV0pSv4DiYWPZRibW/i2iu8BrcZnWoI3GUCVBazUPhu6GItTXpZGNzxM1f4dg9C4qUyK3eEuL+MnyAiF7Fn9SZjhpp9Gi82mhiVuDy9na3I9hi9LgHyG+4kdMb/0iC0seBmDp7FXk3DcDcNZvJ+Q3gS7inXBhGKDNLSfpOY9oKjDbUgeCRM59I3nbFiKOGVyGQKV+hHlrGT9ZdjOGKLDtjT6+/MufsnLsPKooUNVjIi460Fxm0k122i4fRTI0Kp1JlGU+ls6ehYLGD264hz3XtHI48Y/kw9vwXLRRGOiOMlEuY8x30WdvIb7ISbzgJe/twpKPYpu7j+4zP6f6BwXsyTgVzWHu6H6KdZcfRnfZqXbG6ZmK4Mm3EpRK75mziPQqLkQDZO8sJk3j8gsFYvZJClkvi8MqYY+XkUVlxP0JYpPddBR7uf1AkAVX6Tq67vCbrLa9BsolyeYl/syoCv8TX1UOYOgHQLJQzKnEh6exm1WcnW0cH5+iRvVSwODzzx2kf17knYt9bD21i8PW1XzylS/SF38Tv6uTCfs1tA+EmQj0Y1UcNMT2sHBRaPGXk0vZYr2Zz9b9He3TYzxbdROP18Q5+eNncBgmECpZbxrDo9Vy2hOgK3WKDf1ZVFHiTL0Fs7KPtKsf28UGR4/PR+zCF7Dk/Jh8c5Q7KggTpnvCgzO7wJuywN4phTo9jFUv0pfvBcD72sPogkiBApbadUwVJ4gED2MCFKeXC6KDZy0VDJsreaeucZtgI84gAs38E1lcdW/SYJJIHHXgXZtg7HMOFh1YxgOjn8NcgCOR+1GtBs3xBeQqE43KEE7FhqLKBDoSPJK8hbJ0El+mHsE3xJNhcIs/A/6VysllzDYmueqYg7UnCrg2irQpdQhLjlBwTDO2q5bGiAVvWqI+kuS11msYsLUyc6SFyq0TTOhLMBApP5FFTt6NfOE5TEsi7C9zELWk6EjLDBidnD1fgyeSpabjdQxBxZSqItOxC3QRptdg1B1D1SQOJrejmiqxJ3aQ9dzMqaU3Y4onSASPcGzvEtz5AEOeQ2gFkfmKAOZCFEHwkivcSlx6oTRFS+hi2lqLtdvEx9f/PZbJJN964l+oTsc5s8XF7JpqhD0Kao2dVz63hP25G8lcU09GFBBDOXomxjD32jm0cjU/ttzNPSkr8/034JAULJXneLO2nKaUwfo+nedqVqMmgzhiYNBA1fwuyufmsVwc6r7+zBziiEa0S8RZGyWdCOD5jQ97NI75pIufbLBjLeTJW6wEbRIfeznBg9c20zVZZCCuYjl2N0rOT9dCnkONHp5Z8U4C+SR37F7F+IiAxzZFxNaBI5flyv07WMhJcKPxtl6/lzL9S/yXGAsd5Hyvm6/v+SLToVJQfOoHJxj41FcYu/196Pk8pyeT1GmQtKU4Ny9iAJN7D9P88u+pM6v0RQ/TZLmMzNDH0RZW4wqnSIlnyae6iAY19PBW6tUUV1k6iDvCrJ1upy4/ywrpPAuajwOFOvYJJY99r5jjptYyfrytkw1nDtB94TxzlWVksqsRXAMIAgi6zPZwLao5RsC7l77CGpZlnejJIpHYKJeHO7jWsol7y0p+95VKaZxiMb2AbrYiyirOqz/Kl++18pP6l5mM96KZrRiCgOFwcFDvYX/qXRiCyOZigoKWJWiLYgBbp05jDZzjbKyDJ8c/SuTlSlyNGX68vZn3b3by1dp92PUEui7zD9vvpuCwsUJ7Ct/EO4gO+HBW5VC8ATaPvRvNPsebikpShC29ARA0ZhtPUhY3c/0xhYIscN3RCt4bipGsOkSo381hFUKFVWRFOyc7VjLga0UwDB5IfIC+4lIMSQZJZI15lPOmDoLhWrxpmXOukt9+p1CktW6IFbNzJBQ3d8xFWXoiQ+hYyb8o3reYHTNenkw0sze2kV/Ui7gzC9gTTyEpQQrOzaTrbmDP+quZU69FEVWE1BmCkUombF3IohVXKofmcRLRSxO5Cqobp0sn0lCLhzmmY3a++y4Tj1wl8thlafbObETQDIRqEz+2fJYznibu7H2B97z6At5z85RnU1zeexhkkbjfw5BJRVRtaAU36cAZhoVO7DXHAINbj6RIjG3l3ZlS/huzjePOFcmZZE4sqUORRMwZg8BjIpFwPU39S7CHkuxbeRN3ffPvmKiuYVPfxWJ0WYLDnRZUGT46VcAsZinES26l2yJ76U4P8+mJx0iY7TxwQyW/W3sNenYpcXsZjfNBpmo2kopsQJLf3lz8UqZ/iT/K3seHKGZVrrqn661thmHwoxee5kDwcgAeeWYHX7hVxtb8fdzKFHIhRfBXvyE/6iagSlgaDkBsG/XqLMfLOzhdsYjPD+/kr1vzDE8GIFVAiheI+b0g5UhHrsRQS4+6W3IOcg6Ds6EcnkSWWU+BZtc8lfosr+l15DIdmFGxofDT8OO84zE3awYH6Wt1Mdi1kVx4FQ7XeQRzFFGz8HepQ5x0rGahfB+R0c+xNloq6A0GD5Ms9xCUZiBmBspImD2IogtdS1Esb2R+WYRXhF8wa1GImI7gV+rpLdtAW2SaFa4p/lW7AVWTqBXjOMQwNqmGN1IL+PwxrnYdotIR5rXJrdR72/hJ+sNsmOnnbF3Ji8fX7WLqvI8l1Rv52fpVWJRp9hmKQLEAACAASURBVIQG6FQqeVas5Ev6JF9Y+32KiTqCUor9aZnuORvVUReevELCkmTjuRqqkyMcWmYlYAKtdRIZndnJbkJVIfrkLVQIy5AwkA2V5eIIx62dPGO8+63/drK2ASZh0FfGxjEbO5aXgn7j2hS17GNVJIFJM+Di1EDvwgRnH2tHyQnc0D7BXxjfIH3RVvu63U/gSgZ4c8V3uez8Fvas3kRv92Y2TiYYKQ/jC5bxU+e1ZAQnkqhRdOpgNjHVvAR9BrZEJ0h2+imqUd4/NcHTphTjNTEamgTGiiLFyQ5wiFxvvMKp3Co+aP0ZPe5Byn9mwnLZ1ayd62eC0rKL4DIR9U4gFw3EaJ7gOQcsgfXunQg9Mxhjm7l6wYcqiCiZHZze6ESubSa9YCJpaIRX1LA+OoV70KDxQQ3LQi+qZOHVq25GFiQ+dvIQnok6DizNMxOAsRorN8/MszKZ5yXNAQLIFFgvP8LOYxb6RR89yRF+KXyUw4treG2ZnzmvndqIFcNzA67MOFzqyL3E/9u89MB9zE2sIJs06NlWi6Pazt6hMJ3uQV4dX4U3kKJSmeXZ2W62nHofrkoFS9KMItvZ+0qMDWVN+OLnmQ3Ogg3ujvyOHzWt4em2zdyWehoAJVfJ2oVDnHd3MZ31YC76MFQvzapKraJSq/kYLVwgXahCzScIV2rUFhzojjxtuTQDgFfIoQsafZWHuGG/hbQVHrreSutcABQretGPKGZR5QzH5SX81ew9/K+mH2Kp2sHw7O1klF4yagJVLwWrw3qpgCao9RiUlCxW1cxZbz2HPaPIepGiqNDXHOdcvpGp8qWc0kfRELjF1IuXDGNeN905M9ucdq7a+H1kudQFGg93EUTFtGIxT5Qto06fYKlwmhfFm6lsifKF7jUoInjmHsCr2fiF902KGHxlyoMqFGm0BFlrMTBlJHrOBXhz+Szmoo9NgyYqklEkA3Z1GbzTGUdqKuId0llp38PLk58BJ4SM0lPMp6QdnNBaEVAYN7diMgpohsxA+yKsC3Pk0tV8yTPIa1oNBazU6SnSbplX27vomJ1FLSvgH3KxuWKc44nVmDMz/KrQQdrnoXVsAHcqRtfIGfobZKxqmtrpXpxdK1goExisNTPp9zG35l7SdhsIAutPnODA2nUA5KrqeHlFkb7mO1FkgTv3/J7s7BVcZkoTX6imra8Crb6GNzQT3iqBj/zoFYz8HkZvT6N0GygWgTtOv449rxFLmpAUHbPTzEJEoXXL97B+08sL2z+GI5NGS8tUtu3mQqGCZ+eXkV0TIHBsBVdYHuDhm++lVRji1twTBBUz6nAeYdCEZy5OsWYFJys3c7TOzHoO0OE+zoJ2N4FEgtHaempicd7XZ+bIzAh4u8DQWep4AZcc4bW5z1GoOM0t0TeIh24H0c/BrpLkedXg66w6uQ+pMINaeA+y5e27vi8F/Uv8O1LRMP1738DqXwqI7Hl6hL9NhUnlVartMZJFH3VNTq6Zfpz7kx/hxelt3JDqQzD+N3vvHV1Xda79/tZau/ctbfViSZYlWbZsuRfccadDCCSBQEhCIJCTQnpy0pMT0kghJwVCCSGQUE2xMQYbd1uyLdmWZPXetaXd+1prfn+I75x855z7Xc64Id+94/KMoTG0ypxj7b3Weubc73zf5wlwuvZW/Fm1vGSZZnuija7kfGymFCdLxtDKXqHFeBPDYhFwDEMsi+WhNq67dQlffLUXaeIqANaGZ8hNXmButo8d7h9hD7yP0+gYjDlISKipDLtHL6M3axqTaZS42sNtb2os7I1xoF4maIkTfNvc5MbwEvo0M2lDAmf8E+TqFj7o380fc1/mwMQ0OaOHMAGW8BTu0hTrAlO4xErqkrkIPUqZYwFVphXsj73ApiV+DOM1dGZUuir70cUPCGgmhvs+zVxtGmsmgarKSCYDmiGOc91+JN2MFrUhEKxOFPFrk0qqYjZjZvtIA/nmHqTsq3irZiVJi4PvtX+RxYFeHrBtp8dzhujMCjQljFVoWKp9PGm+lq+YPkFmywjjsqB4Ksm8ETdFoTHCTg+rp+7FOudFxjtVOo978dlUuj1zWRhpo8dWjlFkCGKlVapE8QXQ5TKqRQvGySQX8paRWJWH860LuBSVzwZmiChGEiUyk+TxudwHuTH3z1yb3k9L+3ZuMD7MQPEgWUE3GfdsqGfzyX0cc9TRWh5gJM9E7UgeumxhoLgCgIZKiag9+3953qTROFUtEToXOkGWOTtv9t4t7Gxix5utdCzYilV14XDcwc8/UoNjIAbtQXKFjabyr6HLBuSDvyYy6iDpTpEfMZMxRJn2OigMqEw7jYzEs0mfzuaFkss5Hy1iVesFXPkhJuNeDvoXUgtkd2ZonaNRfyCfy6u+h2zUwQZFIsHBwkrGVm/lK+4aGlIRTpcUkTIaWB17k/GpQhQAyYkrHuX+B77NVPZ28syjJORCVtgfpcrayFS0gA42UuRXIfctsuUuNrb6KBOXWBl/kkX7Rmmdk8uRm9fzI+O7J8EA75D0JUnaCfwCUICHhRA//A/HNwA/BxYBNwshnv2bY7cBX39783tCiMf/Hhf+Ht4djHV1gGQHIePJs+HvCuFwaGxZ6mbPBTCbUmzKUtnQ38LJvCb29OzCPm7ifYbjJLwLGUn3MeYp5PHaXQAsjhyhYaGMQQNX9h7MkSxSKRf1k/3sPH+IC+0NSMZ7SUdrkVDJiTWC1sca+2yGTb3zLU6P12A15ZGQEyQMYeK+drZLQQ6V/ZUFL2ZY2SEI2WH/Mol/7f4WfxJGHKh8PLQJKTQbipowTPNb3zPcHNzCH3Nfxm68gElP0Th3FTkpP7enjrPM2EVjOkZjZjtJMlS6VmIz56BV2Ki2Zxi1aaxSBDW+JBeCPv4Ui7JcHmE0PQ9HdDXl5vOUG1/mREELuaYIypsfpDyziaQIk6WY+PXbJQ2SEFRcuoxfaWup2NpNj62S4shpPjTVxMNFN3DJdDnlAx7kVB2+qJc2Y5qpuhmCUhb7TR/jg3P+yM5hJ9JUHlPzy9j6UpjztddgyRQQ6NrCy1m9rEvb2Guejy4pLAmfZ1PiFKGUmYjBATlpUnmz5LpAa2FJ+BS9znlE7W4url3BUEsuVSEHojhKQNE5P7EMkS/zptjBVYaXOVOuENGuwTMV48mCWzDVmMmbHMYWCzI2b4xQdoirjxXgSELT/PnossySznGaqvKRdB1Zl9BkQJa4uGYloTw77kiMmNWEajAi+5P09Pnod81j0qVwukqieW4NS7oDjAUEQQmWTmTIGO0gSRjtW4j5nfRX++hXPLiDXUStExQEdYYqTLCyiFdPXUl7Th7o4B6YBmOIsCWHMV3mA1EzUjjNuKGEL9fexZ3+x8mzTeAMFjJ86UqeUU1cn+9FxsJ0OkVPPphTCSZe9eKKT2B0S1zVmMYZDeBJQsnIH6naPUZGPEPKlMasaox4bcxpe43xOeuAB/GIfUipQqqbPSw4O0K6SnBhVRE1vZ0INQNYebfwf0v6kiQpwK+BbcAw0ChJ0ktCiLa/OW0QuB34/H9omwV8E1jOrFPY2bfbBngP/6/EaGc7kjIbV19xRQn7/tjBprSBG6pfonWgmIJMLZVHh6nLL+XqmRb84TxSIYWRwstQJJk+p0p+zM/Xxh9mZiKbl7f1YU8I7pzK8ItiQThnlIV+WLPpKJFzVloaBKYFR0mNX8etyutsy3mDXEsEtyFOM7XUG9rIdyYICy+d9k4GHYM4M2DzxsiKaKzsEPQtVPjqlRLz0wXkTbo4QogyKcPTxguUCB8I2Jf3NF+KXKRMOolDdVJu7kZg4MSabcyL9LCo43GikoXl9hcpUdYwaL2ebHMuL+lxTMUXAKj3jOA2R0gmnSzNmmJcNuI3TvHF6uPYQ7Bh4hQmMhhcQ/RN+hhP5FBpMmHEh5QJUujLog8QksQhj2BxcpxYygFWiQe6H+Pq+l9x0VkDwJeif6W7T6HZthGHZZp+qRqAg9IOSsUA23MOcCZzL65QIcdWzpqDS0qahH8eY6VWQvYMQ7YS7pL38LnyV2g0+vju+F1snj7CB0ae4Tcb7wLANx2ibN4Qn2r+GQ8u/Dx+Zw6bVj5Gql/lp/mfJ+m30Bpdgiw0pqUc9sfex+sV63hUKmCJ+wLmYBNh71U4B5/g9RVjWF2jVA868WTmk3SYaFq0ieywRml3P5Ls4dxcM5pBomDCT8rqZSbPTvZUmukcO/UDp9Ey2fTEstCReX7uEqYWhQkZrFS3BtnVPM6zbg9mSVAY1YgZQ9jVbJLuJch6DJEZJme6B3/uMgzyHPKjo2CogCwzL23exYdemyEvKRiQ7Xw320RO5w5Wp3UkXSJuklgxaqLbrHG6qZ571u+ltWsrWVEzTpuDK3WV0WQ3V3ue4tncT4Mhi8fe/2mqey5ilWxc2RhFws1EuZmSZBRZEkykq8g2t6ID9ZlpUuHDWLsHCWdZKGKUN9Rxcq0VjLtXk7iumZvNh4nEnLzLcvrvKHtnJdAthOgVQqSBp4Fr/vYEIUS/EOIC/Cdzxx3AASHEzNtEfwDY+Xe47vfwd4Sq6Rxqn+TxE/2MdbUjK/8z/z5AsylGcdrAUHsHO/N6WT0qExsv5WTk42ydcyW/Ofgzrh1upb9sN9a8C/Tbs6kMjWAtjJDO7qSjVOfmIzqleRrvz57NAZeTOuVZE7y2M59z1UnypTN4TX18zfAXqlxTmBTB8yOLeFXbQEpT2CJ3snPffvLHp4gaI1hHTxLru8Btb866Lr2wrABZwC2hdTSjEURGsp8nKifQSy7SLE/x7elRatMpbNIYq0MOckz9CFs5X5p4lJe7P4cCDIQ+hxBGTtLGE7YinidFq62XWpefmKrgtYZAEjxx9nZ+eurTbLRLZOcexZHXxorYSXSTRtogUTodpndiNb++fAVxeTb9rtH/GpE8w6zIjS7Qqob42Jqf022sYPnEEM/lX8VFZw13dz/CsnAL3624i815Rzi5OYv48kKS0r/P/A6LLcSn5+OKF5JW3sRpnBV3E5oJkKmeXMaJJSmumtfKl0x/wSAL8uQgodLTvL52CFnW0GyzYZbqM12E+h0srG/hU+LnAMRkG3q5A8UmeGlkB01zFpLtH0VOpPmT60amyWFnbD9NeYsIz9uOpEUwxo8x7U2SE4JV/SsxOa5mtPQqAu5sNl6YoSSUjTeQgZSOeTDMWE42aTSkcJpo0xSmcIb+7GVc0RBgzkAnN4/8lVEjXL/vUXa+9ixlza+RiTxJVfAgBaqMgoHXqx9HzoSxxMfR5Mdxjj9DbceTSFoCoZtYYD/P/zSnzVgNPLvYBoqE3zKPisEr2Tm5kDVJOw5F0DrXgEUV3BE28wnqqD35QzZnjvPhnDv5tfEBlltvod77BQqs5xmw52HWVZypMB1z6+golMlkeslS/8KGlY1YVyeZypTzcuBbPNx9DT1iNqTn92aTP3qRcbmA3OwkizvfwhXqpa36Axxovo/sSy6ypjII6f+89k4RMPQ328Nv73sn+H/S9j38g/Av+9r5yGONfO+lJjKmU/jmFiGEzsXjr3HUKJGyhBlqvBOp6UqCNlhgfZW2nlxG//Imk75FtNTdjVGNMVq6n5huJ+ywUbQ/xTMbDJSPC7Y1CSZsHsyz0U/acyV+PqHw3IJBhnMkPMLBJ20/wixl+MvACr6Vuoa+sBulv5PJESd5eRFMRPnoy6Pcvb+eWw/p3POqzpp2nWj5Sr4T/AaPtH2WyolN7BUZjAjmEGWlzcgy/xH0QA3FjNPGXAA+EuzkF+ERds45yD3DT3PEu4wmw/dxmlYxGc3jy2xiPwl+Rooa0xFWnQsw051HJG3nx42foiFRSVt4Lk+1v49tFTO4QyruqMoFXxGvWteQNa1RHAix7ewx2owhklqM864gfqsJY1LHEEgxZJ9Lg1hL0mikJ8vN0wW7WdZwjuW+N9ggvUTI6ODGJQ+gyxCxeP/tXsnqFH1yJd92fokTiwQLr3iGsDWfiCfCsFcnZgyxdGQXWY4b+ZeFd3N51Re4u7CSX1Xcx83ZHh4JDdNcUYyQFWxqnMs9ncTjubiDGWqNzSzQL2InhpBgT/p6zqorUI0mgkM2XCM/wnWxlc0jr3Cr7fd8u/sXIJsxjE4yPX0DeryADY3lGE0bEHqQYzUp8qb9XH74Z3glLyO+CI7GcZSBCMgSUZcJz1iKAjGG6AwRsQgOV9vYOnGAnPQ0l/sPYVLTlCaGqYl2EFdszI9eoiIxSppJJpwD6Oo5UpYcbBPZzB/1kzZoDFsyjFsj+GJp1l6Kz35xuiBa4eDgtmym3Cayktv45VUefr+xHWPeJbZoaX6zy41uSjIec9CXHmGe5RAZYWGJ+TRRsYoG82qeUe5EkwzcF3yQm0YaAajuH0Akz1BbcYBL8+y402m6kusAMLuzmI7k8oXUx5nMykXWdDqSZTjkJPWmfqYkPxlJoiZVxOsz/8zPvS5k+d2d6r+TIeW/uoJ3Wj3wjtpKknQncCdAaWnpO+z6PbwTZFIa3/9FA+fKzVzmSLGNKZbuuvrfjsdSKs+c7md1oZla6xMUzR1l9FQEgyXIqaY21ML5RGsO4zl/BbnBfsYNXfykaB5XRhI0Z+0mVZiNHh/lojbAwZ7bAMgVDYz6TIxl6dx6SEI1GlnT+i98a/HnsEoCVYKAkmCDI8Nkr4Mxl8YNgShD8Wy67DZ6S8fJC2fj8E+QGTUil8L53UlWPm1i/fkzJE1uBpbdgp9CtuZ6gBR58jxG0DlEhm3CxMeCV+MzyDwfr6SGGQzovOiC4hkriwyzyp51DDJhyuKT87/O9a1pjiUu8OMeB6lKEz8x/oaXxWp+Gr6FV+TLmBcY4/DoIpKqmc8qL/Mn1zZOjq0myxLinxNPkzZIxMrjWP2TZDqM3MILeLQgF0WaYdlLd/3sdzN/IkjupMQbK3N4K3ANslsnqRj5/JFz2EYLmUp+nONeHa3WgFD+8+uTNzqFv9BJ0GTlYI0N28wnqA/7OLrUxtl5FrafSbGqM0SXZzkAbQVX0iZ2gyRTlBjh08N/JTB3GQAViWFy1RCVRKhvCXHAu5qVWQO0FtaxWJzltLQWgzM9a7oejKC4hzDIfyE2uQaKYNBvY3Hg97TPXIHKAtToAv5cIthldtJUHmTSm8VXm3s4vPgailWFTp8PU+cUJmM/ctyJbnORNZbEkW5j+9EmQn2C0ulBEmYrM/YcCsPjqLIBRVcxiQyN3s1c5n+d/OQY01Ybii7RVHSWJdMbKUi6sKU1uhZdx07FiSHTRctYBTNLNNB0UGQMHSHkchOZVTm8JkAYZVLuuTS6n+UzY4v5l9o4RxZa2XoOeixjrFcCvBr5LJOJOn67bQ7lQ2kUfZa+Lh8/wxnFy/bjdsr6z9Awv4Ctc9PkTakIAV2JDcimCHavh0OZlTTqC6kp3w+nYWrAijZPQl1oYrlzNX7/06zOOcuLge9R23EvZLR3M6T/jkh/GCj5m+1iYPT/4tz/qu2m/9D2rf94khDi98DvAZYvX/7ulqP9/wytLVM8tNSCpkj0BSWMf32YkgV15JTOSgO/er6bNWP7WWNsp2RhN1OtXtTkQszuYRJZbogLSvq7WXz8S1jSccbtWTzuW06rHKPG4sMe7OL3PjMT9jokewsWRye61EbbwnxgFDm3FtfCpcTkDK0piRqDmd0NkN4QpUQ3ktlXQON1F8mSNA5OFzBQFKU2uILh0gAbemOkgkamMXOjHOBUThXFk0HaSueSlTXKeamK/VKaH2NjbPQS/1yYg4KJj0lmfAaZ50jxgM2FDROL9CoK0ivQxSBwlN9mlZOPh5dzdiHpVvZ5dGJjc3nFNCvaNs84wHbvJCczYwwGlhLM1LA43ctnzc+xzNjFU6UGXKKMV/t2sNHYi8XdTddoHvUlw/xk/AY+GH+GfHGep+WPYnR4OV02u+g4Z9LMwv4Up+p0+p356LLMF3seZURcg9mcJjZWh+oYRQI+cCBIkakXe+FJstUAn6v+Ihv0QYpe8KAoVn67y8UpZSOLpBC7J39IzHEfh+oLuCL6Z8Y81SiqjmaQUdI9yHqcEetihkx55DhSIATliUFa3XNY7b9ERpEIxGrwSEYoBLcIEjZ5sBZEkaIqUsZIovc+FHcT8cRsOmuXNY+O8WU40zGSBhOqQSXmcfPnVW4sSTP1F/q4YiqPRNLOqaoJpMCspaWh5Bls8YvYotsZTpn5ysUuPHqAkWkPHb7F7L/yCpZfOM7ac4cZzyuk1G9A6BF+7HiRZxMGjMnT1I1GaSo30FkwRv1YF0NFGxkxtWNw1dA//Rp6+hJmzz2MuS2zIZ60jpZrxhr6A0bbTcRTTq6JHWFPyTZOeAPcNwYbOsfYU1dFfnCafw4+wyXzPL65eCe3vR6nfCjNou4JXl2VQ2FqjMoZPw7jXmL9hdS4jrEzK0XQZWB+V5RptZyUsGPxdJOMl1Kw/AB3y6343BOk99hYfaGZiNXCnLJJetQWtOIQZyims+h5goqZjxo/8K5ywjsJ7zQC8yRJKpckyQTcDLz0DvvfD2yXJMkrSZIX2P72vvfwD8Lhjik0ReLy42+QM9lOSjbxxBc/TWB8FE3TibffyyJDG/nLB5hqXUHLxWX4p+xkTCqD9ny2TjWw+sVupp1mRublUhCboT7azimrxtyup/H1PceoI4d1xc9hLX6Keekm2uaoNM+VyFbd3CTfw946iTsrvoMqYGt2iMKro7htXoKHqzm5wMLHgmFGVB8DMQ8V6jLc4Rhzuk9TMhNhyq0wUG3DqanYamNMuuxoecUsNOygyaDRKFT2Z6Yw+fJQhZnPCQsODS5JB/klcZZJY5hQ+VbmNn4X3MEXLZcxbXDzm6qfcFfdz2milpyISsQ1S2RHSldjQCVTE6Zfc2LOPsJCRxM/M/2WR+w/Zplx1mJvy4gBX10csxLihFbHC3ad1wwzZDDQMNdHg9HLIi3M8ZU57FvhQEhQ5g+RyhzAICTq+2JkDDKOdIIPjb/EwxuKeHRjLgKZ0TkVlPpVymdULONllLWWUnrejSOVQVgEiywnkDWdRb1p/C6F/fU23spZwYb2FkDiK2tuAkAzyEhqFM1UhmqqBOBfi97PoKVgdgCS+nnUvY6tSx/i2YVLMHqPUuV7DpuIcVbMDn4JlwM5mAIpia7b0eIV/6b0+T7HASQE2ekkqmzE5XsBPc+KrOr84sefpEfZw9F0HKtmoaUkhuyPIRkCqNFqrJ0FxJsUVkmX2DTZSUtBMUZ7hg0rjzM/Nsq5urUEXNmcXLKeqTnzUeasZU91LTF7kjQaRYFJ5o+qBJ0ZfO48dIMN1bOUROowWmYEybEZTTETshkxaCNYuvwIj5lIzj3E7D5ElpmpxOza1VTmJm5nhvCYg5xQhi/Hv06BsY07au5n2GPhmQ1O1l2KEXJl0VPoYOXpAX5q28Gt0a+youjPrHWOsXgqgC+QwagK2hLX41WGsSiTpEOFKAp4XX40oTBymx1/ro+OaBlGSWW18X5uZC8baaCSGOHcQ8ji/7AMgxBCBe5llqwvAX8VQrRKkvQdSZKuBpAkaYUkScPAjcDvJGn2qRBCzADfZXbgaAS+8/a+9/B3hKZrnBw9iS5m19ETrdNEDg8z3NNDX38D5lSSxa1H2XH4RRRdRQid9uOHeeXsPjKtaUo2jRLs3Ml0653Y5N3YhMTBRBYX/bVcnjhN2mgga3OGM/WbAJg/1s9Xz/2GwrETvF4zGyoasQ5hzkjccNZGzCpx3jfFkmgNXy75Bb8peAK7Zufy4a3EB5YzPlPOxQvbaPEtJFXcTaGm0TlRhq4YKeg+x1WvHODKU0k88RRj890EcmVmPEZWFowzU7eezb7dCCRswO3RXnYZsskzZfEwNnZJJsxKJz+kkHwpyKPGb/Alw1O0iHKMGLlQtIa6VS8S7hIoqVEiHGY0FCPtMqHbFGbMVjzGKCGfgUMlK4j4PsOVlc00WOZjkjR0JEaFl88mX2DfuV+wXOrkjKjijYpfM6Z7+IX6Zc44r6fV/k+YhMod589SnB6jIBblW9b7yLPNirhNumarb7LT0/RYs7l+9CDTgQy/rFMYz7JTOZrAlupHUZP0xVdwhg9iiZsYMRSzwf5HLlVkmPAoCFnizDwLx72bCeVEKZnKEDcbMad1ZE1HKFaQjAhltgjosZLr6bKXoegqgUAPtuNhWpxVHBbL8FaEcOVO85GWh/EEDP+2CKqMxEFYQI6jp/LoN+cRSDkpdAzwlP5NBlx2ZClOddQJuRYsgQhji+J8qeoUYvXP6Z1zlIi9HDmQxmUcRZ/aQSSyFEkIfml6kNBiB95MFJvHyOV9fXw49SiqxYhjo8RwUQVPrhH8euMcflT+MXKFA6OmoEkSXXkCIcEp6+xCtmStJZ0ax+y8FrNxCRMeZbYAbPIYu4172Ty8D0fgr3zg+KN4AjOcnlOPEkqS9haSkaM0CsHiU920ak5usPyIPk826ILOfCMvVZp5sd6KlNR4M1nCg6Hr6RIlNGj1vE/7Bt9L38H8ziiTBjPt4UVoUja9yVxA5tSpWzhx/GbCoVwyFRmObVnPvrqdxIUFL2HaRCWKUPmgdpiSqRUEIu9ucuM70t4RQuwVQlQJIeYKIb7/9r5vCCFeevv/RiFEsRDCLoTIFkIs+Ju2jwghKt/+e/Td+Rj/38BMRmX7mQ6+1T1CRv/Po/nevXt55plnSKVS/61+n+18ljsP3MmznbPlEZHDQwT29fLkH17Ekx5iVfs5FF3DoKkouopiUWk68CThkfvpU8rol+cQHlyLEAI3TibMSXoVDwKZyukR+vIKOaGvZGnfPlJGA9XxDnoLXXx7/e28lVuOS2hMGKdIGQWTN4XYOphPSk5j0A20W/soDCjcvc/OmvMjBAYr6L20BBHpod24nxvaZucAYiDEnA1DrOobJmQzc7SqkJ6SUuYuWwzI9Bf6MIoUK30j5Ji+idvwoUctgAAAIABJREFUJJ/V4myVTCT1DPtH/0RIi/FdaYBPSCo9opDJumJezL+e65Wj5IgIChJJq8rq7hBXDQucZy5hSe/HFDoEukBdnUMSI7FsBwfEDlq87ydpW8Yr3hv449L3A3DRWckz3u3kqEGQdTbTwbDIhZSDQM7XaDIuwZbUeKp6GWnJwIZgI2PGHOrSbfS88iPm9O+ku2aczuJZH+GRLivXTf2YN6I10BMmPRRFGYyRO5NC4MWdmqbKMktezqRGt6mSj9R/nd55YfpzeJuYBXqOjb8s3EZvgQlF07m6IUz5hAqSAkLgjGsgBEKSUUSGBbEDcD6NKxrAFQnQo9USA2a6XLia6rjh5DSyEMj+JHIog8XUhTXvJUBB6HYmYrnEzE5azEWgW8hxvUZ58kpUm4H0hE7OdgsnzB/ge4P38nxkGSJgRVJlNmpDqMLMN+IPcWfzHuyjcbJyZ0lui9xCAUF8mV4e4laWeE+weOAUKdtqwuZcAM7NXQpAe52Z3iJAQNgWxUAKyMKZ9TFkxUdf1QwH6s0gMqw808aK/LfY7tpHtf8Uu5KXuLlrD5rZiK5J6G4LS7Me5lO8xjFc3G26j1NLlyFFMjjeGEQKp7mwyEEo20Ruzyi5GRl0CwYlxhOmTZxVa3hW28AMDrqqs8gYXAStU6hvrx0V6xJKxkFs3ILdHsJqOo81WsyTkw/xWviTvKZegQWVLMJ8O/Ua2d6c/9b7/9/FexW5/0B8rXOYlkiCC5EECU3n/up/XyoJh8M0NjYihGBycpINGzZgs9koKyv735okq7rKo62zY+mDTQ9yedEWUkNhWpRBEsYIqixTOTIbkmhbvJ6YZGGj9gbxi4JMt5XmWB3Gw1a2az4EKhcNUQotJ/CnN2EljnkE+qsK2PrSQRQVGnOrSdhnpQUkKU5YAVCwTG6n0Pcae2MS6aIpFsTnMmIaIa1kuO0tBzUdXUiAb3IcdyiMNTmr+563NIOWkfCMJTEFUxijBtqX2jFVJbFOXkuweA/jKROOwAJCTj9F7EcIAxaliZpUIweD9XREL9KrZ/gVIcLCTY0hRJVbY3fAxldrbqc0EuWbqQyfQUc9n+K8gEURI059PlFPDVb3XgxjVQRza5BSOhG3l8fkOzGk+zDJXo4aNmMwZXis8BqmJBO/zr2VvcpGltDIjnNNoEJV6zgDi0pxzqhcmXidh4p202xfQMzsR5MM3Db8PKVuAxcT27i/7m0jD11DmU6iu4yk+zPIQkexJ6AdjlplysweCtPTPFyvs7xZwZaS6CyyMMFKstMBVJPp7adAwqyl2Ok/xp68y7nxeIzCcBJbm0ZvQRbFfpUx79uvuhBokhGlL8rWCzFOVUcpHu2nPzfI10dtlCdcrLWXYtIDlE6FGO3PRhgEroInkDJuEkB1cIBpPc0cO/yruBrZPM7yeDnn52YjCR1lKslx03peK9mNMj0rXme8EMAlYuhpJzY1xdz+OPPzuzk2sgCfdfbXz4FsIx3OHC73CuQIGJ0aGwqOcU6sRaCTG7vIgZod1J4+R9TgwaxPYkpn43e1UTDtYii5hrRwIpPmqUVz0CRBbqQZc0ilxBFh6uI2rulZjdlwgsvTffwukMJk1knJCtuNFjYbnyXhETxUezNWPcVlDafo0xysGGjgj3U3UjMzyvcGf0Rz9FtYFj3H65lcGsZm72UGIx9V7yXQUoTdlmZUzqNQM5JjCdMnilgYLkV191Es9RGuHsB7KJ+kotOb2MACrQODVyWo5SKkNNMzfvLz370kx/dUNv9BOBeO8cJkkPvK8tnlc3NoJvK/HL9w4QJCCHbv3o2qqjz33HM88cQTnDx58n/b7+v9rzMSHeGuxXcRSofY+vw2XnYf4Zyhj0I9m5bCCpyhGYRioMCc5K3l63ks+BFUSaGjrYoNE8dZ5z+Apk3TYIxRNP0Uf9FXoQuon+7EqGm0OYvpKMli74oavr/iFkK22dBEfaSb60wXWWy5yIpQETtb1rLtoIE4KuvCS5Awkx+xsKg7zIElEnvX5pE/MYkkBI2razh97RzGq3PoNRdjzWh4/6KgZgvyPjxByYZxTOsPI7nHaEjqqF0L6C/yoskyY6lPcT5QSLGtn3xrCq+jmxfzd5BWTDxp/D5lZRoPTXu5diAOIY07F9zLcGEFtSUOio1GZAQnLRr1SZ3U5Haqpuv4eO8o14/PFov/k/eX3JL4ErXT36QkOWtxeKv2CF/PuZufFt2FKhvosFXwR9utfGDtAyCBMWQjalOoHo+xPv8xrkq/zOj0ZhrcCzHrKRYF+yi1nOXJegsZ2YhvZhJHyyTrjK3oC1zIQqcqNcRvSv9IdlmEqYTOBW2IZns3R9Nm9npU7MnZ8J2kaxw/9SEaTt3E6rGzAKh9KfZ4NzFfa6FwZhhbzEDptMRn9gyzoymOapCYlRyVQNWp7Q1S5g+xuUunYvQShuQb2DU3fd4ZGorfZEZ3UH/SjhxMo851k8y5gduPuXGk45QMFlLXmeDY+Cpm1AJWGRsxyOs4X2HlCm0PZWKE1/p2oY/N1mVkyWkkXXCzeT9viJVUaDaCN0H81hR/Kt7CW1OV6LLMg4UWjrstWJwZurprmOreyHLLOW4ePcX25hSbz7jJWJyENuZCyEb18GVIhXdwe203WlkjC217cSlj6JiwxM6CbGJed4yZNeOE+tYx076L5VlPstH9MCstJ9nobyRlt2LQM5zyLOGn4gF+Uf9RrAnB3a/9hH8xfZfKih8xkAiwvSnG/Zfup3naCiKDNlNEvW92MmUxTVIeG6RZXUQ0nk2fKU0UhXY9l3MWlSGDzl57huTQFeiqibPmL/H02jz8hb0cXj+Fnt2KiszyDY+xtf5pjBbL34l1/mu8R/r/IBydmf2pd3uRj2UuG4PJNNPpWZ9PIQTNzc2UlJSwbMUK7r33Xu644w7Ky8s5ceIE6XT6P/WX0HRUXecPLX+gwl3B3Yvv5ukrniZHy+YZ7xuo6CS882kqrkROxFCtDqZxY/THmTCYGXWUMjfehycvjN2XJB7fzwmbzDOF1xNXZotJlio9nK1ZyKu3XMuZkioCupWy5CAKOtNZhVjVGbypaZaQpHbyAkuPN3P9iTRfeFZnZOBZJtPt3HM0D4OmM1Ywl1DJek6tXEzPHR4Kb7nAU9tuJM8ww4Arh7DNTtJhZOpWDYtJYEhkkc67hBy0ExivolTZjHR+HYfXermUNcilkA+jrLGr8ACt7kqSipUnzd8nkJvNtWN1BFJjvKp3Iw3FCNsNfKvOTkOtmx0JI2uM03SYdJosMnmyiZVDV2EZX8aFwUXIhiB6OsRaYzf35MSYsWSzQTuM2z+B1BcHqwHVYWV3/yV+F72T9RwlR1bol2bDJ06lk719W1l63M5IYAMnnCtYHOngDf8X+b31Do6XzoqLhS9oqGM6Hwo1secbd/Gx3j/zRTqRSy/xgarn0PKtHMz28VDtDgwDMQZTSYK22ZCg5E/zBXE9nUIl2ZXBcCmIoSfCDY3PEjwZ5rDipcjYxu6sb5EWCcqMF6nvSczmx6c0pJRGXW8fAHmTUeoCE7iTcfy5nyItVRP17yKlW3nTImPXJbLsU0xm7+bbd38TXC4OVSzjK3O/z3PdVzHP1k+6vIJn1pmwxRNcr/yVGkkljsDQFSZP07kirVLj7cTnNpCUjFSZprDn94MMS/KbkHWdiGU2pFnz9jpC7twAM21XEpmexybXs+SKp5k34aIsOcze6huIzfGwsH2SMXkujyr/RMTbwUbXQ6zz/oQBTysZgxlZnUG4nye3OMnEhevBME2t+RAAZjnOrVPnAChJjnHAvZE9i3xYMxluO5hAmzDyTbEa3X8VcwLVrOweJR6aJBU1oasTxEcqyZE6kCWNEjHFJ01/5tpQkNtiCg9c9l3qig+iIxPBSr0ygYROr2Kko/EGmiy19BYY+cOqywjbjRTYz3PeUc1NvRLrR2Oo6XdXZfM90v8H4WQwSo3dQrbJQL1rllSbI3HSus4LbR34/X7e9ORzZ2s/iqJQWlrKli1biMfjHDp0CPE3K/qqLtjc2M4nz+yhM9DJh2tv4+nec3T9NYInlMW0eQZDtIR/nWfhfXsfx5BOklOhcbp8AZl8B3afwJNlxV0WofKqAeZeMYJFHmHX9B4iBjsguEocZ3lbDyeXr+AjJ/cyMceLVw2zzT/70iw3XYaqmDCN93Pe00wiPUpeOMZwNtT3CT58UOXnv9eoPt+DoWg5bsdqQGC6YgBv3RCdHZWMZMrIzoTJ9/Zy5ze/z/1f+DDWrPl4BrYxp+GfMYbmUNTxab41+GmmpRm0ly9iCs1DrT2B5+ppUoqdCApPaVu4WjlBiWma37lvYE4kzKH1R5AvfwFPYJI5iT6uS77BA20XyIoKtuY2UW0NYRESY0kfL5jMDCkaw/EC3CbB4xfuxCTbCMolfOJMJxsPvErj2DI8MwG8qQDmtEbV2TKMkkx5v8qqsEJSCLJPT/LGQD4v9lzBi9Fa4toZWh1lmCedDCpz+VndFaBIuLQptruOMFeZYs7JacyWPMqVOswVryLFoT7ejLNGRXeZEONJsrQgGVmhIzFbaORIHqM6aeWh5MdoT5SwdfQNJASvRtcQTOQiud5gq+eXNMoe/mCzs1cRzG8NYWwPY56KIswKc9VCpKL5TBYXsMC7mfWZ7xC1V5NKfYR1MSsH7BFy5Rluislc2xDgtv1N1PXG8a/KJrowh0jYSHRDNhOlj9CpPkHB6K/4auSHZNJGaqZLUXIsVBoG+U7i11TEBfct/S0Rl0BGx1f9NJIkUHUoKhhCIBjPTpIdNLHbOUt4PscozrVPYTaacDiGKXdMMD7/IpebXmFEKuHPa27HoKl88OzDTIzk4t9XwSsj1eQxxGDFn0hbF2OJHUNxTFEwsxCvPsMW5w+xpHW6cvMIqnnExldSmJhCkxR63XkM5vhY03wEmyphdq2lduRDLB2+ijnBOrTEMOcG5yKbNMzmXox6PrbebO5d+HvWqFMMWBYwTxQQd/Qz6M/jquJmQGKH3MD38+6nqDZEj8cPq5vJKAoVsQnuHHuafU13UR/pIO/iBNc2tXDzwAhO67soscl7Mf1/CDK6oCEc46b8WSPrxU4bEvDKVJD7e8dwnztFlaxw1JVLZipEeyxBjd06O/NftoyTJ09iNBrZsmXWP/XgTJj+RJrI1LPkWXw0DEd4XDLw4cnzeC1ehCQ4uOQk1RefonDCzMHVSyiI5DPuzqZQDLN90V4Wh7pxZw+TijkwWWMYNkYoP6Awp/A16gxlZAszx9avI0eNEzMaqBqYRjBrCi0kiTctNnLyCjmT38iAN05Jlo5BF/xul8KSgQXUuJZiaT9GuCBBYtsEtdZLJCYc5ORMMnwyl5fc11Md7wcgEDHjLAwwKFVQeGoJsm5iyhTkwPS3uSEh4UPQLNnYt+UePnlpitTa34EN2iosPNLyReJYuMEwyPvqf86i8DH6Nx6kVhbE/ZV8ZvFvKbMMIYREwrWIGe7Fk9PN1Z5JOPExOowaL9lSPO1MYxVQly6kI5nkm+nv8H5exut3Y51XQjpi5HoRwdnbiX90HUYNgqOVlJ4pQ1NkrDrEQipajhXsRjr6owSrIkjtYVrGTBiLMiRss5W1i3qaeX/FHkS+hVRfFFt/JQuG/sTUAh2SZlRFZ4vxDZ5d80HmB4b5ycA3uHnip4gRDZEzjiP9PFnnimlcsp61xrP8wPgQn9By6dbyeejk/bQsruY+xy0c1xbjk4KcS1Rwzqzh0qFqKM2xYpkH1n6Ibwd1KoxGpLTEj3yz1UBaSQGX+oYJ62YeNf6A5rxaouO38+RGJ36XDBYFPV+BAhvm6DGElCZtqYdkM0ZPgpH2a0marLgKI+xs2EuTbKDE2Us6XIDZNcrG8hdZVtxJbKqCIWMQVxwkJGZKoiyZMZO9MEgybSHSsZPCuhexBOaRlCDb7adm3oMksXBM38BC9wUclWHkVp0r+p5BNkh0RXxENSPz5i3jLUkmP3mED/vSqEequCHry5jkJGHFyeA8nQNtP0eoNtZ09fPcoqUgBOZMiiUdh4iXzGCb3IoCCD2MJLvozWuhOh4nVhAjk9uA1Lgef/cVWBIHMSUzmKM70cUYaamX0YGlePQO3GY/X5P+RGnAz5OJ7/F+33c5Gt2G5NS5J/wQu8cPExReZD1FehLGr9sLxgyx8BZsTte7xkfvkf4/ABciceKazhrPrMyi06BQaTPz1NgMWZJg3fQoSlkFf1xazUda+rizZQCTLHFdnpf3b99JLBajoaGBTZs2Icsyfx6bxqBHkBItWCNVnBJlfObUFEmnn5JUKSc4wZR2iuqpbJJGA4PeF+n3+Viix7lHegRhkMiYc5i6eC2xSB7e8qNUlrVx0eRkQbKTD5u2M66dpc0TJ04pjVl9XHHBz2S+meywCUlIjBhnyGSlGMiPs7DHxTUnI8w4ZWp7CjClUnh9ZbgWV+OufpGM+xy6KYbDEWBqIIunnLfRvGAVvzz7A4SQaDlRRp49Q2NpFULEuGQY5CfVJi4UOombxilvD7FOOLnRaSE0YqbzhTLMC3y8KOfysijhw5g4Mnce7fYKPmp+gMi0nemz96JG8vDMPYRY8hSSLIi/7WKEIUp17iUm5s5lhSThcPnZN7Gbm0at2BEsEWb6T8ZIlEGDM8zm7BE+7hljqOfzMD2HOcYwwiAzOFOJ0WjGqMNSLc3xAjf5+bPGGRPuFOPB1Ri0OAngSJEFdEG2f4JdL71OZkMGy4oUgY9B6nA3stUHTJA9vBvNEmJTyZscEtvYIb1KbTBKlTREq1bB6s6T3N2Q4Ms115If8/NP+Q9TqCbZqZzhx+Imomuy+BEfAA10ZHZJfexUHuYt7Qps6cWYRxWOCcHZfIULU4Iaq85TWoiLnlKqRtL05Bs5tK2Umkst5M30c5U2xB98mxn0LaBkdA+XjZWTG6mgocrCuKUJXXYT9t1F1shnecRvp27GzcA8iZ2HXyBpsGLWknSrFygZykG0h9hRe57Jcz76WnOx6FYyShpHYYy7FgaR3i5ADrfv5FDUTUHYxHp3DwjIyhqFjIRqVNgR2MuqrJOUliU4OVQFcYnoihIWqSfpaiqmL1BEZVEn97n6qehUKBV/QZNM/EDcwGVaEJN6gpvyP86+yIeovrSDwsIko9lmNKPEkuv6WNLeQEI/QFPsSqbsR7H4arhywTFkReXZCQ/X5HTh9x8l1LeeZGAx+9dYyA0bWHPqaYJRQcBUQO2QwlfEPkolP48UXMf1Uwd4KvpNPqT+kDn0k2M/izeapnuOmSNdXyDn7qew2lvQG2swWO3vKh+9R/p/B+ybCmKSZS7P/q9H59enw0jAGs+/38yVbjvDiRSfm+xmOJ3m9k3rKc128aGCbB4f9VNjt/LdnlF+3D3AHXorV6afR33weUJ3HuaAP8zCyScYRWeiYjM3HR0g5u7FFp1DyfrfkBWVmVF18meymHElyA0tRuR2cI/0O1LRPL7i+i71o/1s7BmkfNeTqHIKowzeuQrmLge2la1Yyg6w3D5DfvstrGxw0i1JqDluEu5isnTBfGWSk65+zKqBjeetFAZmEDW7ccc7AJVW7U1WVys0ux0ETfXsbCnitNbMg+WfI1CWw9LWk1wXOUpCX03c6KBwcJx0WR0dtgyv21NcKFyAKdXJGwUO3ndplFfivRhDUxg0BVV38L6hW/iVEmGJa5CPhxfwmexK3CLIzN6bkCIeDGYP5qImgj2bseW3Eo4XE23bjdXXyYnhcrZlD5FbuQ8rLiRnmkcqP479rccwO4uY7ltK5WQWY9PvY5NmZsC7GMtYDQbbNJ76J4nqZuTejWSGV2PQrcSMQZJLzpAsej/LT49TM2ji15clSLUYkIyQK04ykHM9yBIVw41Mu4w8bTUhjQk+7xfEN6aBCdAlgl1biCrdhC4O8Itdd2PVJUykCAkHBqFyNrKS32S58Ns8fP30Y0idNtoSVubX9YEL7uVevCLC3TM2/EaFW1wrsIs3WG/4MU8lHyOGQk5QY9pr4nk5RludlUBOKUgSn+hNEb70ON9ZcRvjpbl8L72Q+/3D5Be/jnfiGZL6EP3OPFb1fplwPEBo8XnitjXUxKeZ9lyBP/QGh+f+ldKAhi8whSVvN2+kZ1gXOEXgJEiKgZHj+QDIlhR2b5zkpJnc5dMkdQWQsMgqYnA991gMfH38OBaDwsqKDhTD/2DvvYLjOs9s7Wfv3TkHNHKOBAgQAMEkkiKpQOVEyUqWZFmWLSd5nGbsmRp7LMdjj6OcLWmsnCzJilQgxUyKIBhBEETOodFodKNz3OFc0DV15g91/ikf1X+j57JDde+qXau7vvdda+URFY25TC1v2G5jg3KEmvkk+foJHiz6KnKllw36XRimFGrOnWNl7RCXjCzjjCn4lSZe1DXzfO0h1i0s0Tip4pUzXG96miNpJ189Wkjf+iX22TvYdGYRRAWTeZxr9L/ggxon6bIJRAHQNAoKO3hXcFJvmaGibCc/q7uGkWIbd2V+R33nFL9q/SG/OfJDdrAfRMhg4Ad1DzCcr+Fb4T/wytDX+FnDLdSF8mjAQomOSse7CLYw/uN3k0snWfe3Mp8Pi49E/+8kpah87vwUWVXjnlIvP22q+C/PpxWVp+eXuKrAic+g/8/Hv1Nfxg2ZZfbt72fr1q3/mTn03foyvllbgiMdRP79VejS/4uXLQzv/fTrSKs3MZ89iqTpuPeNBhLOYRBAFXPsHb6Xa0dfpWYqwrQziyxYMaVHuc2dQ0JDNgewRfJU+E5hcp5Gb0ygB1RVpKIpxLkBLyO+F3HYk4hZB4GWJwmO1uCRGmlbu4/Tp68hnLGjCSnCpgX+6UAtNXOzKIKAs3Y7YnAcVcmjBKf4/lU30iNsBOAN9yhp0xbiFifrJ1/g64tT6MUUy/JNNFhDBP0DOOJreNHey0D1CpypcxiWfkLUcx8nHDq0eCVb0xNoQEEpTCt2lhWRGxt2MjqtMWhppC0ZgGwzkk5Ak/YzMxOkUNfMwol7UbN2Qp4sRfJr9CSvYzsHWe4vxCfv4FDVHFSBt3+eibZ6HHbILC9RqhUgCAJVI1vIymY8nc/yrnkI28hGajUBg2JGQyNiHGXOsxZ3Ns0/Rix8v+ZVOmIjjK14gObEBJmMmSmdiJhfZLzwPfyXxskaRJDhRFGWNWknkjmKbn4tdl7krZSDt80P8OPo4+itg/yRq5ilkO8M/ZlXfFs5WbQCQYyzdvE8ekUgazQQ0bkoZYkqzc+dWjV6sws5p7I3GuSw41IeMR+h3rIHI9eyZzFBqM7BGYtGxmvHktWwpDJsSA/zrZI+bEtPEK+4GlvgXnbGRU409qDLn8MZXUHEOcjrK/5M2NWPpqlsDHn5THyO6dW7ecp4H3OBJ1jbe4KsW2ZF23HCw1cy7l1gVeYcFVsWmJxpYSFjYUvHURbipRwYvpi44kJY0Fhd2Es8VMeg6yzPFB/i6/P3MNP2ezTtwtKRKgnUDnWy1VyEbLGiU8M8XFrMeLFKXl8PAgytXE3NoV4uPzKG3azybuSfeNri4TLzTqoEeErcxqMLuwnlzHiNaa7x/IyUZKbEa+Hy8SpETeMx3+XMMsE/x8dZN5ngWvdvUMwqfz75A7xSH3u8G7gxspsKJYZn8Qy6KY2LsqcB+P7k77hROMC4Vk5UZ2dP6Tr0WYVOfynD/Jhi9Xs8dO5JHEKaeZ+TeMbK7F4jG9zfw1F/gFjZHpLyV3Hx4fGR6P+dHI0kyKoaXQ4Lz8yH+GJlIdX/yyDm1cAy4bzCp8sL/sv7YsMhJj44ht1uZ+vWrQDkZudAUxnSL3D2zc9zfzrMsbCNNxsN9BsNvDi3iEM3hjt4HFUABZmYdQrZsIAgq8hmP9apjXSdy1EaTpKsTfPu+gDlZRnKDRd26z2ixgOmL1FnUlC3gZA3MT+6CVNxP3bvErYKI9GQF0dxEm/Pp5lr/w3l2+YoOb2DsP49Vq7cS9/Z7Zx0DlAWgjXdF8pOos1uQp2/pXB/koWEhakNjfQIG9l07n30sRyn2jaS1+n5+qkJ7oiupMjwOBmljYNGhQ5rF8PTPXz81UcwylmOVrVRMvEOITvoU2fpj+9AsYo0x/oZsdSzypRlRssD0OIcZbYpTUjYiHcqik69cEYgp5rQW1dAOoeqOjC17aP+UDevu9YzaTTT89Y69HMxWivLSc4tcd+xXzNYUk1rX5bOujxvJo8i2C+4jQXZjGAJMjq4jWiZyk27xhhdcSEfRVND9NSXM2Ws4vvHZjDioRqFzSPzrLQ+iFeNs2rrawDc+N5jgIHeWpHaeYGFCpkzeQe39l6DLrea5fz7TBjHeVl3G6uQaJi4gvnOQXbZ26lNj7NucIBdjrUA6FynoKgRg60WfcuVnM/+hV9nf87QchEdRd9iODWAomskrrloj3aypKtks+NREvJhbNFbUHXbyZVbUCSJa47GGfKPcWPZHIJzGaN2GCGaIeS9D2Myy7DRBBn4/tIO/tXxMxbcfaw0KbTEm2gJ66lKNJBVF/mG/kccDnqwpZy83xzmlJjh11Ixcw1pjJUzKJrA3op15FNPMTVXjnv8KrT4Sl7wdXLtooVvnI/hEPIkan6LIObotQyTHbmHuLObFu8oeIO4g3U8mM2i9+jJ6QVGrTLt2jTHxEt5beEHvN5Ux4M95/lgpoJusYVErUCm7HHKakPcktNjGMtiFPK8EmhmRcccXn2aqkAK25SXrvle/lq4nb8avsxlvVEe3DrEo2d/wIOTf2GPawPV6QViUoxVU8OcMxXzetE1fHLhdSRVZY+wntVMc9/8awzrynk51c6j67+IKMAnjsyzUWliTkkwoP6Idv0/M6gV8Ez+WoZ6nPyrsRG3UkR27DpGjVO0fsj7NR+J/t/JvnAMsyjw+5YqNh0b4Im5JR6qv2Cs0DSNR2eDtFhNbPzbeT7AB6+MYun+NjdZDrGyuxTfAAAgAElEQVR3xS8QRRE1nWbqrrtIxUL865cd/HhpmhG9nk93eRCRMOas9JjirMmf5LKEj/VxPcfMVoLSbsqHkwhAsrqZ28wPYQpfcDhWLUWoFpq51XshAjaQL0SvZakzRQklRMrPQUK3ltFUKV5Vxr1ygfprZtBU0JJODgzuw5wpomb7LCa7ir/3Bryt77BUdYpJJcAXztUCwxxuq6XiU+P4nlti9XGJoVIvj9TtoCo/zoYjBxA1jbXDvVziuZJW+28wGMdRNCdz+QexZzOcj5+gwO5CiIfIGEzc+tYT9DSPgR30kSVSqg4EeLX0RnIYOKUB5KjPjZM82UEycBvV2/Lkp8y80/Qo9oyXnC7NcGEPVwzdR224g2jQzXPeawnVHsfqfZ1D8bu4bO4wE9HjdMyeQlBlutd1cJnrWc7Fb0NnXIGmZTEV7EWSqkkE67GKOS4bvYfpFTn0wMuWLFdqh+hvuJeK+YNcGm1jKTtH7cAkZ5KlfHPHd7BYVCJ6JzXqCOuLFrEcEijyNxLROwkULTDCFMdi1awumCSW1/Fw5AtcJWSpwYxtaRVCzs4VpSfxHqog0V7NZ279K/b+NIcdpzi+8h6utNSAoLLGrefA+QoKnCsRBRF9dhcXH/0jz120DsGwg7FkB7Nqng7PADNJN5KioNXZAchFYsw4nQiuXsScC4/iIiIOMFBq5PPzKvOigoSEvu4N7iyIMxx1cWd8DUHTPFWpAkTFiCVaR9I+iutcIWl3Fqehln6pn2XPadzWIElNQBI0PLnnOZqTsMoZ7gqsoQGJtWcEMo4w18UdvGbNUXf+n9iaUukxTNJrruDm8ycR8h7q6+y8oxvFbuvhq6kpZsuM/EORSkY8yjn1Y7xc3ExBVKamSCLqNxDLZyktf4mtpXH0EpQa86zIDRDCQtzjJrxynlDWQfFilrXTcyAI7Ndt4nyFiXmvjoh1K++6dnPD0n4uDfXglwr4sfGz9Hr3ENLNk3K1c2SxntGyF/FkDdSHP8mnDK/xYOO/YFqMkDGaueONx7gkvwHsGgnDHqyZLpa1R7ldixNdMLIdHQVGCxPZAWpo5vD5L7J5Y/pD1ayPRP/vZF8ozkUuG1VmI1cXuHjeH+a+sgKqzEaORBIMJDP8ckUFwt+mVAvjUU7vnuJTpUcxq3HKhg+hqbcSfvJJUksBdt5STk4J0JHN8gfXhcJuFYWsLskum5nvLSX5xdI8GrA+4uHlKS9YrYipOJbYAn2xStayjN9loSSSYuOYgPck9K1vIHGyhI19p5irbaR+dBpzRsVs6qWiU+TNSBfDkRra9Eep7hxmcdRE2iJjrbChqiITBUe5eOgznPKHKHF3ow+ZWTtuQpYkPGusWGbzWI7rkQs1muZDbN9/lJXVAnVlNzApT1PRHKJ2ph+DOE5Mvp3Ty6VMxfcTzS+RUy+4c42VCjNyKaX+cTb3ujnV5qRfd+G4zKMmCIs2OnRJPNZh9sabWRs8Tng+RqpohsrJUwzWnSVuvmCmuiS6lp8M/pKT1gEKcjmW4m1szj6B4XSYv24V6a+2sKG3jjG5FIPJST61mxbjFOOCgeXgYSTDBrxly2Q3H2dnupT02C8xL0fYvPBZdDovM7ZBJrQG9pVsQBN11AWH+CAwSiA9CUCkppS5oqr/vE9u3PkGoTkbpmQcuyWJTUlStVuldV7mwGVvsW3pq4j5On6mxCg0FBPVFPKihMu/gZbyvdS03kOgaQHNOsTnC6I4A1fhs1lQVRiuegd94y4KtFJc6VoUTeGI4kTXVsaBrmN0BVzYIt10hyvp8Pi5IdvNC8uFTBVUIqbz7NKDQ1iiIjHDlNRFW8kAh+QEs54AM14RWQ3i04xkK3rYMvoxgkMK3YEk1qJL8eSdFFghdaqdM2E9YkqlccsiK8rHeWjOxgveN7ndGsXhX0cuF6dbmsCiGUnqUsRMIYyyE0vOiHXJjQeNT8aMODQQBZFNmQo25YxoUhdbvX+gTTdDuRYgKnsQUfB7S7CJMQKnVnL/0JOMNX6MDqmXYPwLaFYZIf5rcgtmWutjzCZMuKYkKgxTHA1WgDlF/9ONZDylFNqHaBX6eIlr8MsDqNIWIlaJz0+/ja1xhNPHm2lTRtmtdBER+wnp5jGqBizBpwkUmshKOeatU8RCGwnZH2DCWQXOKjrOnaBmMcSY7iAVljux+TIcH0lQZfCxQrLQa0hzhwrzOpX7jWW8oqncnjMgfsiL9B+J/t/BXCbHWDrLvWUXWoi+UVPMoeU4t50Z462uBn4/vYhXr2NH4YVVPU3TOPTiMBWuGczqMln0rFReY/QndWSe/Q++/SkTM+4FvhszIwJ7C/4JV97NsvBzWpdbSKQL+Z55ieK0hbmsE9fMAJpeT11divmpHIoQoGgyQk4SOVtehDM7z/o9JxGQaO/zY8pNkTEaqT83yWRRGX9ddTGf7nuLjUeP0qk7xcT2zxFV15N/O8Tui+MMbohz+WILrlgBonuEn1f/hutL++gUVIILFcixWZIeD2LtNI4nJVS7xOD9FxHdmeJzrz6HqfV2jBU1NBrrmJ/oQad7lLTcTvdSPX3LB3EYrDgKVbybx9FUgcVQGwWTRvpXKNROaGzqldAKjAzaQ1zqClE2rpKpTvFc0V8oirkpGLswOO/1/omh4gQIYFQMZKUcN4YvRZByNGaqMOkkDMkJZuNRQGLVuJde0yBu3Q5EJARgrbMOhhb5YHEYWW9Gzh5lcGWUZ5XvkbA42CbZWD+2l5WOONm8HzclvKaC31aNJMusOblMQE6gSk4C+kJqCq/hgcE4b1SYSEppdLNhzDoH7oa1xJLjxPMhVJ1IwFHAPeNrWS4K8v7C86hqGqNk4eKiW3jF6OXKmXW0xV7GaP4G48UX4jhCJYe4hU3YzCJvL0tU176FAfB1pZEO19MdO4lRCQICqwcLUKyH+GCpinjeSDYpca/4JuXKJF/iZ6yOjnKDsIdc7izZU4XUb9rLslrPIUIY0sf4ZUshUnKO2pxC/rSPfLAZl383mhojE66hz+RDl4nTu3Ah4XOqpZNV5cOkFTer9QLHWOJqfZKlpWJmM5NoJQLVUzdyvvolwrU/5qzeyVX9/4hHDWIz6hHSpWhKiHzuPHrzFjQ1g95QQ71jEUUVaBUngUlGtRrE6FqYOMINwZO8GF9F+9BJlktsuOv3IuaM2MIJ4rNWlmWByniayikV0QZ9kRKSISOCpKGFwvyqrIK0JUnlUhmlsQhXL7yPI5FiXcWLYFAYqvHx8ul/APsQ5zxvUo+FG0tCPDlfiEsxccf0vTxc8gar7WN8YXoNVyXmed9ymo0TpbS4N3EytIv94l7E1GncNUZmJuu4vfNxrh7K0qT7Cs943+Mi1yRDZ9bi0SRySvWHqlsfif7fwenYBbPMGueFrZwGq4nnVtVy85lRrj05wnQmx7frSjFJF366J3cfpf6Ff6Tkei8q8IMCO19bknkqP4CyrZCJgkXuiWa4ITLNjys+TrevEmfwYS6e20hJ+kIIk5p3MqfksU+dQxYNpCob0LXtxmGz07xyhoJjRpbtZpxtMYLteiqfzxDeYMF1LEPaauSdK6+hT6igW6lAQsVRJlIXmWfrgUOs6utGqLmY/GKMKWsdxGDHX84y8U0H9qIwgi9GUNHw6qDZnMAaj7LYWIUnPIw0ZkDuvI5D3Mjuu7Jc9vIRrhzeR91iP6MNLYxEj3OUZpx6K9H8QYodaco7ZOTmEcSx7ZwbX0m3BLU6N2eqd0OFRMeZIjYvjLJ5YfTCtQMJRcZmLqRi6YKDM2mSaZq2M1SR4ONzt1NfNsD+SCFNmSpeNO3klHyEkqiR4rAJl74Af0EhK8fP44uMo6kp8lt+S9e5B6nAw8mlY2iinuduuJtPvPIHhgbXk18rYU3GmPQUsbXlVr5eb0MRND753gFK7D6Gi/R0Ds2AfMFxnQMKcxNsml6iwFTOzf4s3bk+1pbcgc9UiSiIlJuaeW/haTQ0Ai47auEKDvufJ69lSUhOfEKevfPPktN56RemqK8Gi24BY97N8ZhEpyNMsnYnKUVHScSKJOZQhj+GsfFlvLXvMrB/lrwgYZKs1C0pNG72k29KIfY6WUh7KPUtc+3ESXp4FXvSgrPcyMgpF2YgMd+GbvEK3CsehtjrRBCQ0FiXinFVIkJ36o9oqg+QyOQOIeoq6Vk6eGGtsmIdZSWlgMLSzgrWtM5w3KRxOKGjLVLGW65yVHmGzoX1TFX8hV1OBQgz4TlDe0RiNNWJQdSIxV7EaFlBe8m/kVh2IrAas5DlbKaaNtMkOXSkBAO7wue4NxSh2Jyk0RHjtDJBlbUMe+0BnK55ZvZsIB6NYlzWs2EkgM6iMZR3kZF0oGpIeg19Js/FZhgtTuMIC2xuOY3Vthet8MLwOB2uxFE8gKN0gFc87yCLCh8rTFBs0PimV0NvHUOsmueuoJtNs5chCBqbQ2YuD20hKOXBnAX2sjzbi6Z48K44Q029G2P1MUKTt0IOdrn3IxsjTOa7mEWgTvpwYxg+Ev2/gzPxFHpBoFmTUFN5RIue1U4rP6gvY+/+CS7PzLA1NsXUa7O87n+fPzeMcsdmjc8zTJ/RwLm0j5e01UhqMeO1cVAXuSWRY5+5iYnFPB3Z33Nn1TwTk+vJCwKD9nOUkaVdShGdlVBqy3HbIljNESytEQz9Aoakhnx3ksqNEchIZGvTdE0FwC6i6gSeEPVo+iRr54cwV43jyRYz7+jAUKUhTxwglZhkzFfKZPzTCMksC44fMHPKQs8mHXvjBg7GoDi4nexyA9XGZzA0BNhzbBOvX3UVUaMd5uM0Rk28VdZBwOHmW/t+x2hhkhJdigpXiOOJZgz2YlZ6ThCokJhbqOFXum7MurUE8sUcQcWaqKNNb2JvwS38UKfQq/Ty16L3UQW46JyH63rsqIKBZVuO89VxNp3z8sDZ69lh3Io8sIkmFGRB4YzWzeoRJyFHjrN1UR5QP0OHKvDH6hM0TpmJFr5I+8St1OBhtnQX87Pj6JzVmNxhBura6OwfION6lVxmiJaJQp7YcB0Jk4ms0cSfr7qEgmASxWpgxfBxVEFgqaiMwoVZEEQGYic4Uebg3riT61hFVJ8gEO5jgRCd3kvxFqxiTljCEJzn9cxORElG1WSsWpg+cwtNqoAx3c+8ZuaNuRXcUdVHzbk4m9IyGjDrbGa4MY7NHWW0r4rBSAd3OiYJ1b/KijKJxLyLqfd9FLRGMXuzRGavwV6XYShVQ3F8F5ZsirvzzxCsgXTEgDlxoUqyP1CFaPNypU3mgFzHXCaHoAQQ4m0cTxQxEh3DaYBWV4oPFg3k4s8C4DIUcaVuG2Op9+l76Ytko3thbwn1l/s5GFP5nPTv/NpRgj7WRrU0TUXSx6BjCVEVOO99j76CNIWRd7h6sp4N3iE6i/dhURWSLhMofSQUL0V6hUDGSbE5yiqGWBmTkAwKmgYrPX6GgzbK1+0lPl+IafQm5HwhiIcY/mstTWVZBmM+lisllJyErTxOdNaKBPQvLdBQrVDT+S6iIU28fzvmylN0p0W6YyKzSTP4XkPURG4VSikyjCDOrsNQegrDzMVkpASbJY3abAW/KHkK53ItV8Q2Uq7XcTQloLeXkI/PIEgakUkDZXc/id9fQ6nUwIxhhqA+CqrAMxueZtNyG3L2kg9Vtz4S/b+D07EUG3R6lh8+jZzOM18TY/2nruGGkTTb+jKomhdtWEVRGylcGuVaVeCTRd0YNJU/OS+lMHUx88IyNi1DabaVOYOOutzrPG3cSEm2nJLFchZSDSiykTFfD17Vz7UtUQQBCkrMGD3jiOLfQrgA6xEJxaYhrMvz/OAOpubq+KPp15iUGD+138rnpDf5tfArEnNGZg56SZUVYe3agdTzGHJomLDbiSUW5vvXfA0EFU2x8ce1W3DHoGeyiWrTNLOBrQxkWtEreb627YvkS3eSFG/Bop+l0mZgKgLD0RwgcMJeyomKSjQgWFDMGmuAM+6LOCTX8Zi8nZ+Y/4298wVkM13E8sVs0OL0GFNk5+5iLm5ni03AYzSylSJkqY6fl/yKoGuJdecd2NN65krqGS0/xLrxYiyBCT5oOo0gp3BMhjnEHE2YUWw53tzkB+DNxSG+FL6IS+w3cK7oKMWBNCXWAh4r/CsO8SBavoQ6wxpsCz/n0NpvUTMzzNqj/RhkEVEL0HVmD4Iyy6DnM0x0Ohhu9OGYmMQTHmKwro1M03WsHvGjD/QxET3Fm2VXc1SSuOnMMfwmD80LPWSVNOXWRsIeOzlJj6Y3knd6MBSW4NGLzFnm+GZ8klT2U+yRTDQmDjPgd3E+6qOFINPZdiRBpjQyRO6Mi+HCFVQXhyiu+THKsTtZHAthKA3irgsRn3NQ2B4iNmcnNHI5Ok0kiMqodjd2KUgmmafC9QvGjjnQ0MjYBNRciE+4voeaSLLKMcOZU/dztOgwicC9HEueJ5sNsLVwnDXeOWosFk5EahmTHyBr2sNwqpeFsQ3kEi8jSA7AREe3yvymKW4pL0QRFX6SOYhBV0Wp/2JS6V04E0b66i6sJYedOXTyMEwUUmhO4bPnEVBwSlFUTcBKmO70bbw/ryAIlezw/Q6dqHEsdxUXm97Gkatm7tVa9PEMH2TGyZXImFQNq5TjWKiSeakYqT+OvyKGsXWZD6oSrO93Y5t08MeKBA+VJzk3ugJD2sX7ASt+4xJNqo912Upqi0dp1utw6SZIDl3PqpnryA/nMMk2QkIci2YgZ1hmwnOCWftpCs40U2pw0eGNMbLqEJnT7YSVKvYaDrL4Ti1nK7P8Nl3HIcehC2KigQGJS8KXwIe7po/00EMPfbif8N/kkUceeeiBBx74//tr/G9RNY1vD8/yg3M5XMtZ3nEcZo2/kfCRCeThGEvyKLOxYRa1SQSjjRbbWjZLJorE9whlvkww4EIS8xjtKSqkWeIZF6eqr+Xapf2cyV2KO+/AXd5LOFyJxRqmpK6HjoQNkytNbMaKrTSFAMjDt/JacAVt2iLOl/LENhg54lvJ6eGNzGg+9us6uVvbhZsE38vfTVwykT6nw5LIoo8mCQUOYFqaBVXmrU6FNyuvYtS2EmvZ4wjJKvxiO9PmBpRkE6HoOuR8AabCnXRqu5lgPblEJwgyxtrfkfD0IYotKAkTq7ISAZ1AuTLOst7N457b2K120q+V4xTSRLFi1qU4xgLJubuQTDOYfG+Sdp8lG9nIgl7mG5iJ6TTsmkhCzXLE1U3KmGGiLInsKqVLWcG9y1fRqrUyEj+JP93Hs/Un8E5kkZUsekWkavMCUwYHi+ZWxsyHyApZbl7eRq1azlj8NOfsp3m3+Cz2odU4Eik2urfzhvs4cu4AEVsCa1piwZsh5MxRN5vi4Co/8/FGjDxCSeIUW4Ym8IRjFNiq+FKokmLFikfvZiR2AtWYZ4nzDHjeZbhwL1o2yzbhaiZFA35r8MJ9ZDLjUW3oMbJEnvJ0FV55K7sMfcQlDVVfTD60yELaRpk1yney9zAv1ZDQGXBljJwcv5744gxhaSPTg3GMw4vERx2YV5goaJpBMqiM79+MlO/gQtSWBIjERQEh5yQ0V0zSP8+cL8OyrpryeIBrCvr4sf9+Xhu/j65YOVdFRwjHs6iZ42ioRHNGbNWNDEd8XFVwijmhDqFWh7jiL/hHq1HSZ9GZLqLM0U4mch5nzEDMKvNAIMttcpDljEZibpkGv46Li8Psdah8bjlGsSxzzKdRN+VmeLmIWnOQYsPf0mj/FhB6Inkzi/n1RKPvMJ51MqSuYkXhahzKYQr0KTY7x2mwhzgX8ZHNK1iUHF3eGQZjRehVkZzOxIGOCL36HAZFoDJgwRM3EnTmOJVw8IElyFnbCL6sj1vnbqZCcXOX/w7a4iuR7VNUnf4a5UvrSZBjwDjLEWsvqzONSEioxgjuqm4O5zMsF55GZ5ujOXwRnvAGqvJbaKCBU0XT7K4Ypllp5JLYWv6jYCdGxUhMlyAv5YmoOS6q6KSw5L8frfzd737X/9BDDz3yv3vdR6L//xFN1ZCDafKzcZRknklJ4/jZBT4xkOYvpbt5v+4kA8owvriN5fg4xxZ245v5gEe2nqDbkGTZnKQmfwA7izwSqyfqsaGLhqhKJjnSuBJrOE9ab6LX0Iw1maO1ZA5fw0HmFmpJVn5AY0aHzZ1AyxmwFF2YJRSM7mDX5KWsX/kk0rkcrj6FRzqv5oXFHfza/CvahTFeyW7hqNZCpzjCvyt3cl3xCBV7phDq63DXTsC4RFYnkTAZqF4U+G3rvejcPfisAzSmHQTMYcwVT9GZPMaW/gQ3TxxB5xriVGMY0TyDHO3ALRlJporR2/rQG/axJdRIKwnCOZmO6AkqKqe5xXCeQnUt5eXdfLL1ScZjlZzwryKry6MkmzFXPE3KNk1tvIqSZAP/LrjxCPBw0RO0pxqplj1cHdnEW65DdAXW8q3QXXRl68lpCobRPqKpSVTNgDduQi+L9LQkaMKL27XImyVXETNvwJzYy4BllAlnBR1pF0dtA3hmZFonHDgTSYZaW7hCaSclpjlrGyRmyzNZkiDuS/J4ZoxkxsKcYMBt6uay8046zmdxRRI4nU1cbbuUOWOAsZM/YFDKcLqmglVDpxmuOoUzX4orpifuM/GBZwIJCyYkVioVLIpRtmYH6fEdYloP+ryFGBnCYpwWRWJCkqj36QguJumLFNPUGGVJ8zAnFNMvVmDXjSEvZbg4O4cwOkn71CJFyQSFvhBpvYfhfZ3kI82gKwFNBUEg4BjBmSnB1bCLwfAErniG6UYni/FWapJTqOY6zsetrE1MIklVBEIHMGlj5BFISjZUWSMqxHlU28RF1gHqtNvwpotJZUsxh02Ec9M8WrSFpKanXLXhTIqsnM1TmpZQjaUcmjMi42Rp5VZ+dNEXMRtW8aeJV6nJ53jeZafZFMUYMxNMOGl2ZsjrzMwXCTgTMvNSIQuRHJo8i2dbiKL1k0SKe9GnjVTJYRRNRC8qGCSZ4bSFja5ZOtx+ToTL0TSFxfpmzhX1YZJtXG5Qsc00ocsmKYgaGffFkVSBO4400rT0BaRkKUfcPZQLBioTK7BEqzGlKvHnJzkSd2G1vEJO8TEuxNHLMwhqLwv9t+MtG+OIuESPzs+26BrcOR8veXdRlCugLlrBftdxPhW8CXfezuDcHsxSGYKkJ6vFSRrD3NF2Hy7Xf9+e9ZHo/x/gvcn3eGX4FdyqA/k3kyQOzpI6EyR1IkD+9CJNYRmXqPJt38Ncdz7JaDrIs7WHsAz5WbMQYP2WGS5LiVSnmlmXyVIm7Kcv30W/vQY1L1AdTBLOKgSrbsKRHqcwHELLS1ijATIzQ+TtXqZlH13OGNl+M56WJXzjOzDILrL2WXR5G8PWWQ4srqZsTxZTLsdP6+7BYYyz7eK30ZXGOTS/AbsrQkB04s3VcntvBHVhEGvnV9jnHcU7mqG7oZy0Xk/tUoy+glqiTW/RvFzG3bEYlzteZNgs0yjKrJqpYfXkcS4aTNGvvwy/sY4dcTfHtldgXHKQ9a/E4DmKaBmgsOADdPEZCiMaL66KcknmXi6TKykVQpQELqE1Z+Nt2UE+78aoi6AvfB+AL4w9wB2SEx0CT1qOMmmcZ8w6Dmg0ZKso8a/jxtRqzIKBfyj6Cy3dc3iH30B0VuM3KxjyIofWlNPbspGiRS+O41O8vvFzSHk/pvQxAIyGHh5372e0MMJMUYKY1cJAXQP9RXuoypZwfWQrISHOqHkKQYMrommuyaQwWjJ4/XYuyWRRcw4anZ2MlLVwjbSWpCHDbwsfZv1kDU9eeR1jBQusHPPTtNjM5zP3k58do0S3CrtixaoawJCkQS1H0c6zq+wAexywrI9QH6snKWYZt4+znLFhEQwIailJVYeUCRPSV6EX9VyTbkMSjUwbRPKuYi6N7cLcqxK3GLCmZZJaBf7MShYjW/EYiskrcRBE8vI4I9VvU7K8hnec79IwHifsMLFT+ATbdaexRCP4E2Yc6QDklxH1Myi5OHlEsl4Tbzqu5lKth2isjKYKL7J6PQX5OoyanoL0CkrNpSxnFqnXq5QZQa+2cHXRO4jqEkPxIuazTvL5HAUV9eiXNvLxxTEeTH8XTzaPOauxUyigu1DlTFWSKr+FLfZJxiw25ipqCEd09MzkeaPjLAbZiNjrZL9o4hVNpmDmahq1Pnqi9QQ9Iq36IP+jVeGr8jzdNgPvWWz4zFWcqRnFplrYKlRQ1n8/RnkDghpHyi7RMGOlTe6E8CIZo8CCO8aqha2c0B0g4Z+iXt+CTgiwN14KgCnrYoW6DyGb43LbY5ToTpKSNXJzd6PqUtRGazlk62HMNs1CzEhVook6vQMxbWB7ej298gAJJUdheBlvsIaquJOq5Spq6xoo/hD/6X90pv//wsOnHuaxvscQEJg4do5vJR9Af3kRrvoiQrN9pHfLrMzC/urjdAbbyS0o3DV0mofuhjOdUWrbojyTvJVCbZFbpOcJSB4GlAp2CS2gqtSOj9CoFVFRcweczxNQVnEqvpuYUUc6EiCbMbJwxMrUxh5uGtzKQuXbADjCnShz2zkZL6K+8VUOjv4rswkv/7zwCica2lllHGOlbZR9S1soleYot88xHKnn9q43WHlyO7n5XjImA/sdfjJjAuM+JwmjAYeaIy3p2T57kDUfRCkOGphz6tiklfGTQ1m6S76BjmEkNceZttX0OK9k01Kam13P0Z+6lfZICflcjJ3LG5kp2M+sBp8Jxlm06/hS9Fpa0/UM68dojF4o3Hai8l3jFD+q+RlyopFrTrjZ25lkhd6CHo1HXTupm7iasvn1KOT5+Zrv0j7awEWSA4Ok4zXxNCszRyibVclarJy1JxAkDWOzhfMtnyVjlDhe8wfOVn8MTbJzxakcy1gQC7Lc1ZDiqRkLZeFSzrovZ8D+CrCXrpECfln1Et6cly8H76A6voq3HLvYKPcCUK1LUFE+iCRobGEKOHw07iIAACAASURBVMzv2h9mr+YgKw+wTCMFmwpZO3OGM55BAkUClQtB9hq7Ua0XjFCuvBNNH+PV0r28LL4DgCfmQFTy2JMaAXGMQrWWiJSjv+Y97hz6BAvmMKW+GlLJORSrA2lxjolMlpySwOOFoMPHB7FLePmTEZyql5rRGNtOLrDguR2XQeYSh5nx1CL9eSsthmOsT81wZPMPaThgRMBCKZ/gKsMkHctd+K1t5JPvoNN5kOUwcsKPWa+QKexka/ub3DgxjMnchqjej5iQQIMz4X1oxe8iLVRR67iTppJ1ZAv+keuXVyEZzTilbkb116BpUZKpNNuKpmm1HGdWOsWcQaA+GiAvCZwJVrIjBX6Djp0WKKtdRsxA99lK8gNFpGUPb3dNs+TK80FbiKUyH+cKL/gydhr6GJvuYmPB7bxZ8D9YO6vx00AYi6DyuLmElLGCp909ALSebcXha0BJFWA3R4mzHZO6nlz0PxBCZQhSkhZy2I2LnDa72ZG9Bbf7cfSijalsEBGNJvM5zqfbWJK/wjrbc6TQEUo1ssG5k1nZS0XyQqxKNrwBKZelIV3AuGWSRuq5LXMpMVKcNS2gWkuQsy4EScKgryFgXERV/+/9Gf8n+Uj0/x84On+Ux/oe4+aGm/la19foe34/WSHHn5R/4/ZkMY/nRA533cbPprrpjg/TkljB8ebjvLBJQBNgRp+lbdrCa/gIaoWc8l6HFp3BiIwiCRysb6e8pIVLJnwMGKLoTj9Lid/P5kSAtNHAwYYyZElAiie5XhRIr38Jl07FNr+en6ZtfEUT2Th1GeeD1UymivjpwhAWOctal4nPit9hd/RBhs/s4Bdk+JrrCX6qNDEWbOXicJxkcBIjsGshQ6uugpc3bGXOUY7Znucfki+wbfoM4hSoQoCT1cUczHtIGnWUz5/GkthD3G7h2YqbManwAAdYo+7he7Hz9Bs/gz7iwzlXRzQ7i2GphFxymnidxMbY5YxlchwPPYGj+MvkZo6xb2Wee0M30ZFqotcywqdmLudW2zq8moNvV/wOXXgVGiIR0yJxY5i0PsEYcdolK6FMGtPSYe4ayKBZYPwWgRr/IrbLlnk3ekHwBU1lpqQFVVeBMROkY34FunA9aSJETydoEzfgFS6nSRPJ6Ro5U/8wpxoXMCoSh9IpXIrCtVozZZEqtju+yqCxgXJ1lgW9k+dsn+VBfxjJ+Bhfn3yCr5d+g4hJpmZ+AVemAhWN2nglPms/iiagLn9Arr6VZeMiUyY/jnCEygUjE6UpKgJmLjtZSF7So1fypHVJ3tnyPjXRGmbELC/VP83dk59lXj8Ldc3oZA13UmE+N0pCl+athgUuW7yWXS0OajJ1qKgsVud5yjFOXfQwDe4NiIJAlaWQMxk/WWeaMk+ImfMOqqJGUqXVoAtSmRUJ5MuRDCDqPsMG+x/oC6YIZy20O2c54RfYYzIQK6rhS/4HGDFN8ULRC3xhbpxZ0z8gR9vJxeaodrxIofYFbgzfQ0K5AgGJeP5Bmm0CM9lx7LolOtxHEAWFGtNx6lToNTuZkW9laGmIhnVzNDXHGAu4aWWOkEnH0MXLxMYFBotjLLryfCkc4Y9uN+d982xZ7GQ2P0J/5QL9lTCS3Em/zsS/YaRDznBetNM4/hUUKY3Hdp5zeYlbhyuZi64mZ0qwXmejL3SGkKMJZAlZnqaz3kV99jKErEiFbRlTXo+s3QPA+UwZ2cwpdKKdzTaR/nSYkfQ1lOuuJSC7mI8/xZDNiTFnQpY0Ks1z2NItiJKdUUcPfZoeNOgXpwlkz3LRciWTxQ5sWYUpUcJe1of44XaofCT6/1dGRkf47YHf0mBr4F/W/QsmnYmGRAUjtj7eDYxwROtCN7TIQ6MHqLFu5J/pAqA+6eZhSwoDpcyZT/BDXxGtAdAEDV14krTexFlvGUJNio6+g2zxV6IaS0icf44VI2eQ7V6ovwTz6D4ag1HOrK7DkfRTWrpANqFDna9kZv5q2hte4MaRW1izHGAi5cZtVmkffhTNasPnu51heRlVaibueo/PpvM4HTOsmT3BTMBJqPuXmIHDJa2cLmzlNK346lUytSVkBIHXrZez5ae9HGl2cGrlNlomFigO93CRH96ts9Nb/jG+WfcSfzB9lWdz1+LjLX7dXkSnLU+1909Y9q/nJuMhxFScnZEVTEsu7tM+xbw+yFP2D1iztJ4vlP8bWqWGIum5KrqFexdv4CnfO1hX3EQmO8mvy5/lpHUAef56ii2D7Gx7FFVQQINAykLamGFw9nHWT/Sh6WDoCiuu9ghCx4VUrgP6NRRE8+SVQ0Q9F/oHuoZeQ2ALiud+yoTD+Ewpgtl2RFVEEAQcapaukX+h3pzGnTQioTFnD1IqFNNhSqMX51mWPs33y9qxxc/w1fl6lgUjbzif46vLp/mW+Qv8VihkTfAKQqYkk7ZBupa6yOo2oJN6AQ1jeImy+RRlaQ2dagWs1E1LFC8rSKqBoMFN3GCmNj1J7aSXwZp+UAVShhxPNrzET4c/xXR+ikiilLinjvVqIT+r+iU5nUJSiODN+VCVPCXzZ1ksWIHi3YIlMk2N/hIWs1H0JomYa5C+SAEjQ+1UAfESFdHuJS3MggAJeYD7Db/i1dhDvGNZi929gCccIK1di6YN4piu4+PKF0ioIgNBL19hEpdSgJJbQS52BJ3VTb9dYlvuCEnlanKqxu9KnqUrWMZWdQtXeEP49D9nn1hCu7zIix4L98RjfMdjpmEowseKltGHill69zL+ueBNWjMXXOlvGRVoDqJXDPzj3Ce4M/MM7SkbkdS9nFs8htPZTMp0Dklv46xjBFGTyCnrQTqIf/mT+GQ7n7B/G20qy9sLX8Jfuh5J06jNHKPG9gg1NQleiV6CaE+wmB1jRe5j5ImxnM3goZiUHMOic5BQVGRNQCifokWzMk0xxbKHgYzK95x/YfPCtSxZ1pJnkQnHGKoAlZlCIiUHGdNn6EgX8JL9dVbOWlAiOTrFjdxV/iMUdDyd+BPb0tMUHIyh7/rwsvThI9H/L0xOTvLsM8/SQAOCKHBq32HWtm0gN5fAorfz+ND3GZgeB8pps67mtHGEmJLDLip0JVfxUMbDqBTkdV+EQfswgjtNRcpLyVKASz94m0/GYix/Lk92jUZ80Ebvya3UDp4j6jXR02Aln55G327jXHWEiuAJmmo1FFlgZncr5q2LhKfy+Ee7+OTwe9zUvx9Z1KF5alEiIK7V8RvH+7yeuIu8IcSW4Anapiy8Xy9wUfA4kh902QQZg4HdazayQptD8OQ5XbuR2uA8OjHImZouvvxPn+V8RReqzsbb2RTPfussEbOOoc0dlPmmWCpZ5mjGx3gowm67j5dt/8pM9gVuMJ0i6TjKq0crCdjsgMAq9zZEUc/vba+ST53kj5eJ2NIQMwmk7Tfw8Y12ftjv43DjN3hGC/G64edkJBVBgBrvo7xviWFRNQSDikczYq7dx1Tta7Ts1yOIGqFbFLzlMdq6Ezx/0TrsuTAzHg9rB6fYdH4vyx1L7NNJ3P9qD4sVa1EkI0E2EUjEkNIHyRjqMRuaOVg5wZ61tWg4+fzwW9Sqo/y5aTONB4opUY8RzRkpy6+iLCdzQ2YTVtXJiy1n+bPtPh6I/Jx8IkedvAZBlfALYfLpALLmR4snUQUNnaxgDC38rYSG/8nee4fbdZXnvr/ZVu9r7d6LtvZW11bvkmXZcsE2GBccagCTkOSkkRAOCSQ5OQnkhJAQQmKwDQaDC8a4V8mSJVm9bGlr997b6r3MOcf9YzsJN8/NjbkXznOe55zvrzWf8a05x1xrzHd88xvv+F501cK0NUhDdA4JeLXiEAPOev7izHcYrPGxYTTOhtE6TAnOd0Toa4rQ7xnhlvhOfnXTlwhrMV5JVbGtW7Ar3Yxc5sNMDaNm02RNgSc7gt2iEctnGMhe42rsbYyaViy6BW1xBkvQpHLdHL7mFOFemL9+kILfRd49xyk2EQ1MgQxOTzu7bXdgl5w41Y1oUhENwUThBTRjNxcmD6ELBU29RsFMgjgE4bVcoQufxWAsPchc4xm+vsLg4HARoe/nbPhDfGv7GSaETFGGUnwPM9IgX/S+wxZjDl1oqJbTFNM2jmgrifis/LYvy2MXfp+/N0KkFMFFe5BteheviBdZ5dtLeHEMV2Yt2coqYvY3qS5UUCzdybieZTa+kluNP8URSpA1PNxa+R1+FEmy7tppOnf1oFqXx9v99qP0J8t5ZXYliwU3buW7nFpQaXD4mcllOVz7ScZLOitsgh30Ydcu8pzrRSh9AfI1HFi4kynHCClrmEHPEIP+a/hMHUeqjar4RjqEhikZbLqeI5/Nock+8p7N9Ca3geImawbYb/0HKt0zDEXDv1Sck35Whu9/Bdu8ebO4ePHi/9RrJl97ncgjj3Cqvp4hn4OrDVfZ3tOIbgsgFbbxcZyYQiAkgYyEgcmMPM8bWj+ubI4nVx3n/Yn7uW9hE3Yh0W15nj9pPE7GVkvI/Dhf+4e/xZlNYbjySCWYPlRNzekZtAUJQ5E4u66StGYlvWWJZ9xFHLqVlJbnwycNbr6s8sSdB7AKL6ZkogoVRdfZPXwOV8RNrwW6Qk14ywyOso4ZJYQpKaxMD1Gfm8Slp6jJzyMLk9p4kqX6FpZqGxHAS2t3EnF7uevCqzh1nac21JL2bMeVX+LWzAmeDt7Nxv5jjNR0kHRX4inE+KOpb/GN8vuY97RSLuZZlCpZHYvxSfunKZ0qJzwcwKqp7A7dx9tV/TyvKzxwtIdds9f4yt2dLPonqY618MbeT1CyeJFMgZAlLLqOlnoWrTjJxslprldE8Kc09l4JsD+/SOSmBgJvOAl5LmI7phF7QCe3w2RaqeWbxueYUuuoLMzROThO1fwM/rFucFcQyPlYf/0IVw5tYrQYorO0lw5rgYXcOM+2VZOWPby+pozWmWnGqqrR1X8rf/0nVzO09X2Ra3EX6/37GGvUORTfxYu1Jn/d4WBz/1luPfsCnaEpXvHeizI/iTUWJhyUuTc4wlu5RpiSGa7J0BAtQy0WEQ4bciqNjImJTMwa4PHq+7ipYHL/yA/paypyPL+eBj1B3qfTMD3Csc0S6WAljw3+Cv2WSa7aLzMeu86KCTsSMgITISvY3eWs1TZyOfImhighZAVJCBAmpqpi1dyU8jE67hsmHl+DxzWAWYKh5xtA9rCircBlaS0u3cXhYic+WaMoisznJqh3rEBHpzv6BsP5a7hsLSQTo8DyRCYQ7K3x05W7j6JwYpYmEbaX6ay7xK9XOblnsJqPlj5P3DrPVwMvUlBNlpzz/LdJK4O2FA/me7maPkCPuBW1WCRcakVgQW44zRXZQya2kq/iYL7hMWonGhkuhvFos4S0AQZz92OzDNCVvol4YJwWswZPsoHRUpR7pM8TKltkILuJK+kP8MHQlxiX6vDmWymzH8E0YbxQTr5YBnyM12dfwWJxk7KAmo4jvTtVL9VBf9Ms+/IJTnpUIrLCi1NzvB39AkulDpZ8A+S0LAnF4EjDs7xv4qN8UvsBzcUJHhMfZFyqoyK5SHZmEqttC0Jdgay9qy1AkTW+77NFOkZUaMy97wds2rXv58YxSZIuCSE2/2d+/9uzd4QQXP7jLzJgtTFUFmTUNYGa8ZG0zBMMy1QZecrUMiRJ5rRllDrDh4zMBcsUoy6Zl1ek0UUfI6GbCY3lqZBtVIhmthSamLVf5NOvdlM9McP0zT5KtydwHlfw96WQCjKxT5XoLq8gkXYSuGWBq6UmgsUQjsnP4va9w/kak4TXhUNbTUHKkVZzlBwxhK4xEWigGJkmUfIwZq/lkmclhmZjQ+QS1YU50qqTVak+yosRfAkTfy7LVMDLTF0HccmF0hTjZNUOtl1/jR7/SzSlG1kRjhIsu8wnxZMUrjQx5S9nuHYVJiq3nnqBobpVnPJsJ+aswF7Mk1B9+JIxpnx+Wp5bRJ82CK2MckPmZpzWaua6nqB22sLBieUFtFy+jsaIyWj9JsYaVuPMJClabRw+dZy5YIC0dxN5106CVQF+z/U2m0f9FKec6Ak7bW/lKFBNcGASvVrCtivHmK2Mv81/npTNQ3Vhktyik87ZIawqFAMVFD0eEgGNwfaVZPImLqFT9BWZ1hJkqjv5RmcNwxUuvAWDe196hILPT9rpoKhYcJUEHz77U65H4ph2jcXUKLa8jZTTymONEnmbyt3HniGfhZmMl3JHhuJ8ApBQZS9nzY2YYR2h5ulaH6dDW41aVcJvU0hay1gtDRMt2fFrDtrtfjbYj3ClpoWeui1ckFbSW95KdPUK1kx0UztbpNdhxUYZewqNOMI9FOfStLo3stK7hWkxT66uhdsq1xNiBeN6NamyDDZXGSIVpuTyIBWyGHqO4N45VI+N3oHdNDhsWKvHWRhooGTTuFl9h1XmXpqL63HJKieN87xjGSGWWsGCY5BvN/4T7Q1XiQ74KBoRLC6JxpCNWKpEtT3JzRUnaVOOYheLrDUvsslylQ4txquWKnpdKVy5amKSjly0UZEL0mbexISlns9mnuWcw0LQMsZKMYJHDpMxVDKimpgtQKdDcEDJcC2/RMv5EgPOHfTmVzFZ2IxXXmCn+2Fq1X5atYvMRj9ANlfGSd95dpZ/mQ4tzj/5vfzQXc1maZyo5GO91I9TGyVnbKU7cTvTmV041FsYSg8QKy6gG3mUYv7dyUxCSAJXAhodER6r1qgp6ewoFGjMGmyxnaTN8Tqb1HPkkhoj2W5q5gO8ph+kpmjBXvLRJnexmCknMzvHgYoZjNI81sIgOcs2rHIKjzrPbZ5vgmrwEO/HWr2ClS2tPzeW/R/K5nu0+dOn+Wk4zHxZCCHLdAWvcM/sWpwDs2jpOJV4aHGu4rI8xFD6ChGHQsEeYEeukj5nkuuOn+AxV/EV+0l865+hVLiE5alX8U7Osce2Ct/pSyz4HYhPhsmrKj+tvAF/hY2TazcT2jKEkCV0l5VNC7/PbbEbWJns5DnbLB9fdZTTWQcFRwU12Rpuee0YG0tN3Gy5l0xsnLhLJVFRheZVaRFhyoMGrdIidQs91OTnWJEZRlNlSv5yQiaMNDVhTcfQFBnfijl+UnkntnSW29/4KVgtzLkz1OVq6EhkSV4OUTIF0ayTumKYO448RfXMKDVzY1xr34Rq6nz49SdoWhxl67mjXF67A0NWOZgtUHa4C4u6muklg5auE7SHxyiEWknZNFqUQZb2Ofj+5geX6YOWZd2Bgmbya31f5yN1j6FHZU44D1IbTbBhaoBkbg9S2xjjTVsZsewlHchwZt0uJpVqvjn0MTKTCjsmrzI27CMbURgwyvDkZgkYUSqHRzAk0B0uhMWKaXNiFxYW1CTHKlVkYeAoFKlNRGkyYE2yn0en/ysNc1FWjo4Qn+6mxpEkWrcJwxDo8SkW9FnqF6fZ+s7rkC+R84SwFDJk4joANb482ZSBOxPBosDWyhk+XYpwA2cptKRpjGXpsa1nX/AqC9kyUrkChUonARGmmA7xxI49qEaJqsUl5uct5B02qjITrJvLMsMVshad0dk+/JYqlOoO1mgdlDeViOgO1mXWc7WQo983yWDzRY5V9lFJO76tw+Rrl7BXJFixOkXsQoiE2YSpFPFXDBMq3sZqeT9H0gYedTOOqmGuRt5hKmcj5zWxovBs81N4g/NsCUpE+r0YRRlHmZ8Z8QB3eJ+mxeUjljyIR+6i3jdAwD2N1WoQ6XGhs5uTdRNYDB9F3cCNhSIm9yXbubn0HaxijgerypjNbGZYq+R86Dqapw9X8mbulK2szE/QYnyFxdm9XPVtYEqL0qT24lAX2ed+hAGakXXwEmGl/QQzuWb0isf4aC7K1wM+HvZ7cRh2zNw2RqRGgkSpIIIsZQlaM6RKEscXThMrLRJy5cnqGiWrB9NuRynm0VQTt1JAXwxwcFrmI8kMFWEHq+wxVFkgSzo5yU6nrZdNpDHCXnboKbLFDzAYN+hZzFFMxtkcmGIs42Iq5yJlCspseRJGgObKF6hjnGFrHbtKgyQbb6Hx/4D+L8fMbJanHn2UmAbnai8y4pqjTi/HMxjB1HV2NdzPatcW5nMTXJl9AS0ZIRsZ5HR9AuGM8njgKEJOstd/iBXeI1zX16K9muSHnTkWHDkW5wdxZwX5uw2UGp3rc3v43tydzNaodCoKTrXEEe8iC3orN8f38po+RIsOu9a8gNU9h7/rj1mR1dGxUaNXEwitY6k0T0sMXIMnsZkaE5Uhcm4Xa65dI5+bQyoZLMcnUNIEnpxOTNExPW50hxfd7uT1sl1Mlzex8/KP6YjLVC1pvF+7h+v2JEa8hGV6GC0ZpaYUoX52HFtskXxVA55cktbBa6wc6aZibpzA0jwiWEbCV0ZPQzvtGY0yzxwXgiqPtm/gyYM3sfPGl0kdSFEoWDhdfZCX1x9mwV7Jrrkz/PWpL9Lq6cd5XWbDuSmuZjoZMtso2ENMFGs58OwVZHuCo82b+VFuD5cdFiZ9FaTVEql0iP5SJSYyE2Y5CiW2WiZJmHZSeSdfePVxqiMx3PkCOaPEbtsedhjtXC+OsuCxo8dNOheGWT0/QV10joTVwmbbFdpKEzTpE6QWUizlHMh11Qi5jlLVLkatRcoWplDTCUybk5zTi5nJsN0/QZM7RoM/y+HgdTYHZmjzRzDKKmi0xGhkFhnBtbEOnvfsx2ZI9OhrSMs2LIkIqkewYGngam0VreE59s1fp0WNUpub4pLagXA6sFRIlE1nycdnSVslxny15Fwl1pu1FIN9+PUArkKII45zCDVHMF3Lgn2BRF0/d1RHqfAUqaoqIaWg6VtF8qrGrLeM2rpeKtKtlMfXEXBWIdY+Q7T1OWwNk9QVQA7OM2UoFOsusLpYT2B6L4FkPdHCAhvsHyFTcLHCuRdNXs9vHgzyNw33MB0uUlX8TbrDmzBdN1GML2IxQwT0KjQZDuU2MqDO4hXv0K6+xTv6PhYydbjMVZTMEIVSI31ujQeKG1GEBZNqXlQ9fKf5HfKuWTQ1S7Vxkb3u57FS5EnuIIeLRnUSq5yjznma1WaKjCTTZbWwO1aLI7ULtxSlWZrhJNuxGusJCZOsMcTJRVBUhTsah9jnH6RgOlhMKdiNLLImIUqQN1VMFDK6jYFMiKmsj654FQEty/PhTZworuGdQBhr0sVQrJKQskCb7S2mkksErTlMIREuOIkVHWzOzjAaqiafmMQsXMNpLDEUbOazG/6MwFIMSamhff3anxvP3ivo/2+b008kw0zf+xF+vG0Lk54BLoR6EQLe39NI22IdG6t246WWfpfJnzZl+EJvgsVkL1cCKQ6c6adtZoq//XQdH1gzhV0uMEMN35z7dbZc+QtOrJGXE52AK6vwaWcd08LD9/rux0RClXW+s+ULPBz1060m+aPpT7Em08pzkw/j1gVbaw7gczdQKGi8ZLlEh1GDNxyhO7ZcpyOQybM6oVG27b8gqXbCpRkGBr/DvMOFUE3ObLLQMhqjYcZO3qICgoxfR6/cxtnG1VxrWMmBd15h//QC9UoNveETrPLuYEiRyBZG0L0OhKxgONygKDSUX8BdnuD69RtxWKLkMi42+HsZmKynZLHjTSb4m7s/QUHTlqebf1G4FoIHz32NbSsvMTBygCF5JT/t3Mf2viv8xTf/BkkIEl4vrnSalNNOIJHie7fdjWIYPHrnfdzcfZbEokyXXkOLbwZbSqLHqIR3lYUUcqiB84joLg7YuqlCJz+Q5smGAzwYP0Kx3A2yTOvQNJN7PsWAMkNXmQ/nbJzZSRtrbPOo1Rq6UWSsoYkr5+8lhgdbMcOjI5uxOy0sBZvZmAqwwbeP5yb+gYKZRQCmxYpSXK706bIV+UzT8sav79nv4adte/jDgUfYlV/m97+S2cp++xUG5Dae1w8gVG051w44xnowJZlsUwfyu6mEFjGAgsawaELBoJwwcUeCcaORioE+5pqc2NVqnKaVO7K7sZoO7EqJOSnOCSZp2fgshq7QKydQbDn2unRCf65R0By8vfsARWFn39FjHDt4I1s3P4cQUDddT7wuSsm+yPxsO+XV/ZRSlSSnNmOvuoIrOIVn4iDXR9dRNLIcKK7BobrRhUBIUDCf4LQjwmSxCSx2nMLK3lQ957hG1GMHwMwMs36qli2Nt/B969s8IH0XN0W+xScRyOhSgXTxAj5tNwl7hH2F1fTm82yRyynDzV+X/xMt0U041Gn+sPQcEXwMD3rpqb6DeZeCKem0MsGHeAEZwaPcQ1gEyUp2YtZFLK7jfGaxlkLpThyigwUpwZviFI7xAQ5VDrLKt8RwYRv16kUeGt6GKSTub+hClQQvzW4hb5HIp0u47ToJ04ZcWC5+B8uP+0wwS1XSglJaLoEtgBp7kluq+7kSreFSrJZoeTlP7P4oFqvB6vFeVoV78A1NA9C9spPJ9vX8vjXPbXf/ys+Nae81p/+e2DuSJB0G/p7lwh0PCyG+8u/arcD3gU1ABLhPCDEuSVIj0AcMvOt6Vgjxa+/1Jn5Z1rXYxcde/Rjt72+mY07mt1N9/LOpsmegkoC8ko7K2zGBhJSlv2yIr2RGaDLuBmcdTVcfoXJykrTNxu/+YJJ0lcqx6v0kagP8bfrzfHaNhxVpG9PChmvxV/kjo4JgJoIWO8t3Zr4DGyaxOFQauhfprVeoMhxsT6/lRf0tnCUdQ1E5O32E2uAaRoMylrlp5pVzTMZkJAGmamGis5Ol+AIflv+SM4t+xjMmOFzIhsnuGYNDlg24dQe6cYah2/q5PFSDY9DGtRYv1xpWsvH6WTaOXSOdTtPLCKpk0ps4A4BstaN7l4VLNCmPKRsUC820jteQrOxlcr4JSZM4nd3FXWefoWfNGpYcHm7tPsNweQ1WvcR2/xGsrhRflz/PI1t+h3Oj19iUn+VKawu2YoHV4WmevvV9OK0lcpobTBPf7Awd/UtsH+rm6fYbkPI6x6rWIc/GaJbD7M7N8T+9OwAAIABJREFUIqmCT3U9RioT4qnWg2yNXafunhPMaBGMRB1qweSW/nd4rmE310JNNGhzlKUVpmpDfHOFhikvV5L0Di6LtvToldwR7iGja3xu/i+wSDrPFw4R6u1BWCU6L49x7FAbVx15NgAbAtt40jvHhTW7+UTXdzgZnKNi0k9N2M6kXk6ZkoDEIoeefpKjFjslRyNLaoCfVN5AU36RBqaQTBP0IpJhYAnPkfL58C3MY0lE0KpUWmsvc3BkmJRVYzjbiC4UZqUqyFVRDmRWd1KZFQhdYM1VsFiS2WCRQViZyzhJKQ78liUsfkH4zK2s3Pg6hekg9oUUF/dsQnEUMbNuJj5QTc3CDCPXN9PW+Q5L7b1oOQ9l51QiUw7mmtaTWrgbshXQdwtlO/8RUXOS6ekQpm6hZCyTyc1MmHj3j5EDLTibVyK54nSWmrgmj3HUPUZRsrNqeIZkqJYy/w7azVmEEFTJEzSLKK9wgPOhS9gMGxFrhJgtwt6FJfy5AP9Q8TS7FnZzVJnjwczN/PncJ+iVM7ht30PXBV/1e3jjsIE/f5x9c/uYcc5w0jXLdHo9mwpF7FYD52wnrqKHZNmbHK2wcmPqD2jVTDRFY3ThbTzOcUqSzJue2+iyWggVOpFlhd1lY2R1jZFAGZtzGjs2taPP7+NY4SckC0tkmldhmxtHyyQRCujWPDUROyBxS3U/JxcbqXUkOFQ1jCabbAjOYyATdEzxA+9n+I3px/lY/icoLkF8jYW3jRrW9l3GqHAsi0D/Eu0/BX1JkhTgH4FDwDRwQZKkF4QQvT/j9kkgJoRolSTpfuCrwH3vto0IITb8gvv9/9myly/zyIk/xvSb9NqGcbtcjJhb6K8+zJLPwt+NBDARpKQ0r1kv01n1MtVdv0vOPY4YTVI5co3FUBmXD1ay61wPYtrC+4dPU38gzO+uKsOa9/O16Bj35v6Kz4pqHOZVzhZfo3YiTfVCDHNBo3f9rUTmu/mSNIi6+0FkoWAJ95G32sk1rMS6MMWgPY91bBK5VKSAhAR4sznmmxpBlskGqvj+TAEts0zvcmp+mhq3U9W6DmEUEXqBYs1GBuZfxtRtTFVnOLphL7VL49zv+jGVdy9x5eROtHgCPZqi2lmN6WthlFkQgv3OfrJre1nqP8h4PIhZXAOl1cAlrNgxjTSv33IYJAkDibJ0nPJ0HISgNF5NRX0vD+Re5Hywk6utG+ltWktJUdkw2IMkBLLLRkZYsCxOkw/VIBrdDDS28tNMDWMiiGcqSmJFOaurRtkVGV1WHhMw1riBuOLg9vBJbhzponSinGJ5L69STsFqpXfrOm60DBKQcqwpthAyVU44xzncdRExm6Wvqh3/gsKkJ8vWqIvJfAN7nGfYLV3laqYe+icYc/hZDNVhCY+wP/0C1lnBuC1CY9MD7I8dY+/zT9HRPcY9m7P81aYso65mnlHehysxS2oujYng6kYn2fiN1EQzNMXSjLsa6GCcG5tPsRRIMBevZKS8lY3mRZLCjRQeJ+nagOZOc2J9Fd1Xb0QggyShkmLJ8OFDwZEt4rYY2Bc2YComD7U8TE0uwKa5G9lnL2NatNDVs5uQsY7VXERxFPH+KEHC4WHW40XN2EASjCZXgx2UvMG5Mx/EjozFdCMKaTyZEZpeNuhdVcGC7zrl8Q5mu99HoOqvKbfnWYoGOT/zY5I19aSDFhp37mCD0cqs9Rplhos+fZSSXQJ0JAGPbp9hxn0WgM2hVUjmCJ9NniVbsuIpfZAdqcdpDKdp97wPT24teW2A57R5di7uQkbGZth525ikXrOxqF7ljnySb3s9vOEz+Y1YgnHDy9GKU2haAjs5JitMNtXoJC8fQOSCSIpO68KtjDsWsUhhsoqLv7J/nRV2UJdUXORwl+nsCt9AJjCFLfoHKMHvYwl1cW3qi2AEsTT+gEJ6htUVu7g6/RMq52cQ+TBWi06s6EDNLtfAb3UXsMnl2OQyZoUFSRomb6j0pSqQAz42WC7xeP8X2BO/9C/JAMIWk0t1EernnGy+dIrC/gd+qRj4XiL9rcCwEGIUQJKkJ4E7gZ8F/TuBP3338zPAN6V/0Qf8X8CEEHz7xCiZhVkq3nyME7tmaEo2kdASXAx1cdrShqI/wpdmfg+AS9ZJ8nKOtXKQ8NxOKrIVfNd+hdu7X8Qum1gaDtL26gm+vOf3mFnt5FD0LLWVo7w5/yEwnHzDfZyPr32eplg9S/Uv06IJ3BfdRJ02bJKVNZd+/K99s02afFd+DXe2SKFlHZpuUApWYlrt5GwOUGS0QpLqgRGq8jKTgTLKcwoRKUXJF8SZz1Af3EmfN0tEMnjS8ToVE2E25lfzWk2GfNZLc+A6j67/HIFMhK9E38Yqmoif24qjYYCougp3/ApzmTnMmnokJUCFrGFuvIonWccl2UfcbuenyhVSWPEC0nQ/dgn0slY26nX0a5O4GWd97hJvqHswHV6mp9dRQYoNmT7a5yd4u20DcaeHXMCBOm8uv0k1yTRvXOB49yZC+XKui3JywsbN6kUquqZ5ovJX6Fm3hsSSH3cxTXk6S7skUW0MYUm6qT6QxOFZQAiJEBHOD63C01qgRg5zXqyjR57hQkcD9nwTnder8ZgyG4dBQUJkNCQkCoUQd9jfQsjw8vR6rI44wUyehfcJwneVkBRIA5TeYKp7lo7UXbzGebKNVaT7Y2yPubm6qZO4kDAXcpiySqZhJWvjblJailSlG6cosqQEEXnoSPdRbPDg8o7QOTRFqqWI5LaSPWrHtjjJYN8uQvZ+tOkp1KKJ7g1S8oZwyYISOhYBpVgdppblypo8475fp2XpNT4QPUvSvJ2ApZ/JYh1z8iKN68+jTsqY/XaeaD2A0+gEqZ9QNkXY4abcFSOTLCNDiQygSTpZm0q8pYXJBiu2RIznVz7Kh658FmeqgeGX/ztGLohP0kl6WzDyaTxpL5POKQYcZ5BRkHNpTLsL50KOVCUs2hLMuKdw6XZqjQT14jxOYbK5FCde+hVaTBvNiQdRfV8jn9tI3j/CzOpH8fVsIpqrZco5RV2ygQnHBBOS4C5xliIqifwd7LOe5IN6jr5ICynnp5i2P0rWEmalYiBftFEaP0BvxWnGy85wy7XPsueqh8v6DzEtXjqKy9Cnmjp7umcZq9xByWZBDIwz3HIcY2U35678Ma6kTAITea6WR2u/yTp/O1uWVpBJDyGhsXLXJPJCEE0zSC/amYjYcKktdFTdxSv2bp6QymBhnsWEBgswWrEH60yWb2R2EHHp6B2zvBhQkIXAvTbCVkOhvPDL5em/F9CvAaZ+5nga2PYf+QghdEmSEkDw3bYmSZKuAEngj4UQJ///dfnnt//x+gDfOj7AXzoe5o0OK6ZkIucCxF1TmBLIhRE+PX0vbXmDguWrvBJys2CJMbx4M9mxG1BECiO3glcP/CoFRUGSZIKVq1nU7CiYjLr9XIvdRa03DZkErZY+2isHWQz0Usi7cdiS2NpTHE12knOYDGrrOWzXabr8IhdSz+N0uNDdPkyLBVMs7yz1GGNktCq85hJxZwXjG7YwDliETMSeQ46n0b0hYm2thI04sqkxIEXI6FlOrppgbKkKE0GjqONr67eiqSX+29AckUgbYwySt2owvw7FUqTkDaHFI6BOoIsaXM0niZsmXy1qTK05jDM7zf3db+HLl+HRpmi7+RzKnMHkuWlm8ODzSNzsKfBWage3+KKUm8dZlD28xI00KyfIZQMEL8bpXt3Mvf1vMCcqUaQYhijx+LUPspQNMQxYhM6nixkcS3FK6TnuPvIUk5WNvNO5l2lLNfmlGX5j4XHS5Xam662klhwcT2wlafdyr/kSdzYfR5GXs6yrxRz/zC10Tk2SMjy4pRBZbxSHbYloPIddaiZlTRBKVdEgzxIddeDPLQIShXXl3FR5hPDESsaG91Obfp6m2kWyW65jZAbZeTmEOx5BFoIrndtQhII/HMaalri+ahMhq84kV1m7ZpR17jSGoaIU3fTE/KwejrHlTDmnt0dItxURpsxkdDOuhlGYiCJ6CkTyViQli0Wxos5NIGczSFUNWKQieazknbMAtI1DGzOYkos35SqmLa+QwY4sFExT43L/rWwdWeKp32pn1eUIUUuMgpAheRM3mCYai9hMJzPnvs7VTTuJ25bjNIdqkKVIvPIS/lwVYUcWd1zDyHvwNJwkMbGb6s5nmL/0Kwhh4E6upGBJgprHsDuRgD57iQt1x0EuUVby88TYLiq0b/3rM7mgKIwg45NfxpP9VYqZr2BoEeKx73Hx4s0Y2HCKJaZC3VRaTvGJqIaXNH4pwRm1lXS+nNLMX/L7moNIk42LKxwc7PoYN/aUkFHoFTppZYiRypeYdeQ4Ufs1tve4ELYAUiGDat+DpFQwFYrylvZ9bjp/ianWJaqunqBhtESDiLDF8gxnzXZG5ENctXZhCIkr9gFuqPNSyJSxIyA42uHjsZYH2T53mfvWPMT0yUq6ZmKYxWfRXF4u2krUJTT6V6zDKnSah3spal7Gq6M0zzrJXW3kNrvJB8zNHF39OGlJxqF6f6l4+F5A//8pYv/3q7//kc8cUC+EiEiStAl4TpKk1UKI5P/ty5L0IPAgQH19/Xvo0nu3iUiGfzp1mbs8L/JW+iaypRyhxQ8w6u1CyDq+9Grirh4sisRp/0OElTR/MvMHyMj8mALfcl6mPpplc+IUr/s+jKHlKUkai1qAQ4U8vY5udi1cRJGuUB6vYiE3jTsYJz4XpGfwEKakYdXSrN99nNvnrjE846ZYU0V3xTDT0hokwyRf0wxCIOsFrLMTGDY7K264iM2Xpyei0jS/C61yDP/8drpSEkIyWVg1QXC2DIuWJ6/b8UXXEXXMYJUETekbmPLaaE7E+e56PwtqJb+++ENGUxUkrTkyWjmzjjm0aIwKeS2B2ixmKokYjlG1UWdMyjIaCRKu+EO8mSx39/VyPnSR780ukKkoMh7TGJxcgYFCUU6jpVT+sWmBP7Sfx89yvvxpv4/m5BgzmfX8Do+gc5T5njKe4TZaGeWv9dswr0vsSV+i0NCAXTfw5BS0rEEpPYRU7sEWqKBjfpz2Jy9z9PB9DFQ085ve/8qidTme+F7V+2kfnmXGV83z1p18c+ArXKODcVcNn0j/hA9KJt/RP0iNnCTh72Hb3kdQVJ3enn3kFmLMBOZZJ9mRhM6LxQ1krZCtbcXncpNajLNw5TN4dDfz6WmGFTtts1co2znO7Fwb7dNXOLVyD2m3n7b8FdRACS0ukynFCOspbi9M43Wn8UwcJOobBO8Ub40cRDdSbOB1artXM98U5/LQTRTMAoNrJzm0tBpJLBFuDBG2trBq3VESVwKY4zO8v3SegLbAschqrmUayIQqkDCxqk5yFphXe/ltHmOCGp62HKShqZeRga1cLg/intBZcleiawt4fWFsxVm6Yw2QrsNW0cN0hxNv7zxj5W7yFV4aI5vRvKNIZoHDc52kk+380J2iJOs054KsDF7GkvMiOn5MdKkBZ3wVMhI6Jjk5i8XUKHOGOJgyuLEYZmPWJKg9xAwtREufQbZ9i7+rybFLP0ZDKE8mkUQdb8LMX+dVyw04zAw3iSP0SW18fiLCXsIsqRYGLW7cBT9/FpDR3Xvorw38G4aYggsr3OyY7+KC7QwrxqLYCkX2n/JT8gewRzUWfTle2XEFT1rlE0cM0oE91CfW8aP9dryRGNczHdwTdKClsly4uIrIFpNXG2Yw+RFVqY3cnlqLKQmGNQ188NOaMI/xq9gtOV5v2M+WyDu039zF4PE15EYTWDMJ6oGc1c61za1Me9axY91xFuIv4HeFuVOLMjjShJ4zOeI4zwOTgmmbh6ulxV8oBv57+0/ZO5Ik7QD+VAhx87vHXwAQQvzVz/i8/q7PGUmSVGAeKBP/7uSSJB0HPieE+A/pOb9o9s7/eOZ5Atd/wNfzD2AzNGKSgc+2wGfUOa4q19gyv4K+piRhS5wx2wxfmPkklYVyrurQLtn5c+fDfP6FS9hdCktC5+ltVfiLlaweGgDVIO7ahmyEsSpOcnoCVSpRFApGVTW6M8CGq1e5tHkjHpFka+IUI2orM65mcjiWOyhMHHKWkqpQV9dNbsZKeKmGkidIcNUbrAwuMnD2AaIleVnNSii4Wk/w/VKEOyfvwG0pUkpWYlgyKEU3aUeapzcfIGNzYC3FKGh+Plh8kvJzKsJQeW7dFrLGy1hyJynZdvBY30cxKBHOn2Bo7ALrAvto9m/nQ1slIh74WtdRnBP7qLEWOTnzA0ynRt+qTTSceRV7a47DxRs5Pj/C9tDblHtyPJD/AhnsFKrP8qFwhGyungZXBB9pLrMWhAAhWC9dY3DaiZpOkveXIavlqLFhZL2AqVrJNHfgL5snMRvAOdZLW3WE8+vW8HTVR1g/NkStmOdHHbf96//cOj/DDYMXeW7jfsIOF58OP8GX+h7mzeg6eiLV5CrKsNbIVAQmKPcMU/MNG6mNglhWYSQdomTKFEO1mJ4VlCwp3PEOrIUyFjwGVxssJOemuNV7gc7Olxkd3cjc9CqEtLx952djntWDfdSoXoq3H0UqSDi/XUPkUIQNjgiPpz7GBb2Gh5Tv4ZFGkSSTWf0T/EFwlrumV3GX89tocoYlTeXymiokGVRrlvUnM7gpsVR0UGNP8fLMWhYKTWxq7qLeWMsRZScVynfZZYwAgskyGyMuD3OvrUWs9LJYaiefn8WyOItVS+NvkonOhyjaajhh7mXamWDP9Ns05iZRJYPu4Haa8otY0xMISeap6nvIWFw4pSJh4aIj1ceKzDCb67K0yRNckNYRESHUeBQls4il1mR/2sEm17NEZJWSWUkEOy9xI/VmI85kgocrfspSbZoHnRaWTm7jUsMmWhOzyEaOD+nPscoyS8F0kDEDZOUCH6m1Mx25i9rwTmp9dt7c7aN1KM5E1kQJCdqMAa7V72Td2xfYO/w8MgYlLYMru1zHRpE0ZhrcLPmKNE7KjAe3Mp6v5560jwsVZzglytCLNdikLIHqH7A31oHFtCAQKKjExBRVKZWZyhSj1gVW5Ju4VH87o2U13L/4tzxR8TlawgPUq29wwv9Z9vcfI6JrDDZtwhV5CEPqBsCPSQyZ/1KeJ9W7jUNPdTG5p8jQTAuGUIh5DCpqd/BbX/7Sz41175W9815AXwUGgYPADHABeEAI0fMzPr8BrBVC/Nq7C7kfEELcK0lSGRAVQhiSJDUDJ9/1i/5H1/tFgf5PRk9w9K03KZ+UeaPURlh3opolGgI/5HOlu1mRr+ek1keZ6aHDqEVCYhSDz5Mlj6CEgYpKXsrz1ca/wtkaRc/YcI3uoWJoO5HT3+B6bYCEw4YeqiHrt1Eki1WpxjlyHUWBrYEJKokyIVVzIdFIKVC+XBo3HccSX8T0eil6QmxofQtn5TyR/nX0xzpYtfIU8ckthIsSm7c8x9JsByfC7VSrUaz1cZ4UdSy57kARTtrnJ9kzNIQuFzFwcmRVJ+MhPx3z4yy6A+yKn8Vm0fAMCuaVLClrPz2hbuxFmaLF5A6/lwVTYWZpLQdPzqMbRXp2vp/XO9azdnKYD5yaoCRVYSFNOvXSv/6+dsXO/Y2VZM17iRTneX3uceZsldRmZyhKKhaxvFkJTSLVvAFkhUXTyfFCM5+Y+xHoJrJRQkHCePfFUVKClMoqybvtWAqN1HS8w9RSOfZr14h4MvTWZNnVXQYIhG8DR9fWE/UGETY7c/5yti6OcLpqJVazwN+VfovcS9XMLekokolVM+hsTXPMuoVX67ZT0iU8qTiBZJj66CJ2vMTc++nDILLGYMETREJClyRMRaFjao79o6exO1IUSzYQErpuxW6PU+aNIuX8RAyDXNpLraef6vZevEdX4H5lDLs/i8VtMNoe4NXwWvaGqrnF/y16s7cgkafVdhpNLhDXq3jGXs0nipeZKGwk/JaB4/Yl1pizPJdez+hsGR9r7cauREhlbVTYl8XYr2kB2ktRXnB5WKMHaS1O8NjUP7HR9wqdzueZyK/iufEAhuLHIpk02EboT5UjI+h1rUSyBuiInKFpRZZbpWvYlBLjaR/fShzGmw6T1tw0N9rZIVbyRqyIWDrBztAEO8omAZgTAR6KrMW9ZLLGO8/N1UMADGQ6eTa5GqdrCqcvjqvax8KIwJgsYZYUIoEAZzriOGWTznAnbnuUuukrrLHXcCr5EQycABQkk26LjseQaTFV/vlmDxlZoJydoIMEDxgWOoou7tkfwp2M8ZEXv41m+Im3ryCYFZjJGWJeB2OOJuZMNylhZcb04ZeyvC/pw2fIHHGU0JyD9JYaqZVj7LOMcazyGDFbjA+Owb3xHC/Pr2SsIcalFWly9rUsVv0uq2bH2Tp2iRdW1RIO7gRRwmZmKMhuZMPAmn6BQ8VnuGFRcGm+kmPNWRqtaT5ucdDfu49PGU/hlLL0KvX0TrpYUjTs7bfxqd/7g58b835hoP/uyW4F/o5lyuajQoj/LknSnwMXhRAvSJJkA34AbASiwP1CiFFJku4G/hzQWVZ+/LIQ4sX/t2v9IkBfmIKH/vQnhOlmpuSjizi/I7bRpF2l5AU1vJ0z1teJS8sr7tP5AP3FKgqqRFS2YgIWSWeda5Kb2l+gyTfO4mITHk8Yuz1FIedi4o0msvMlChX1yAErKcmJIhTiFdfYPJxhadr6b/2RFbL1bZg2xzLNKxFB1gxW3DKJarGhBeNEppp5y3aYhAN+m2/QfqWG+cJWomtepRgsseVcir/33Mc31n0KgIriEraYm4kKG59JPUT8sp03N7yPmMfHRwdf446yhzkRW01hupOumgauhxQCS18nZ9WpSno4YJYTbL1Oi90kbSp8ecqCJ23httOVqKaMoVpR9MLPDAIrbZ7NpIWLpfwkq6vnaeWT5ISES5Y5ufgSs5kemtzrGcLgHc1Hg5KlcekyvWVrmfY2Qy7FActJtLESpsWKPZth83iGc2sOYw2aNB5+HFUuEeu9icXee5G9Exyt/SHaUpbNA8uv8kWbF1WYSIXUcnwtQSpQy9OHHyDq9hBMGkQ8ChtHJ2ntPYo15GKTuM5kN2yqnuezB76KLqsE8zGWXGXkNRuyaWIpFclbl8cDJYP2yAiKoSKRR2Cjp6aZw9fP0hiZw+NZIJ/3UFPbS2XVAIq8XLSrkHcwOrqZcLgejRK2dCPelJf6iSOUz3bhdke5WPObhANr+Uj5gximFRkDTSoyVbqHK/FNRChnk/MZtrt/SLRYQ8Ayw7XcjZxM/DqaexZ/IcXd/i+S1p0cX6il3mWwwTfEQt7FG2IvZVofh9UxBnM7abOfZqbQTpWln9mcnzdyf8IB98M0WXoZK7VhFREyBSgYKnYNvBYrDjnC1UiQrWVTFNFYNLzMxOxU2xM4lBKPT3RS58txd8Vl+hJljGX83F4zwFuLTbwWsPNn8jDhnI1XZleS1q2AhKyZmCUZd12W5sMTlNJOlq6tpZidIrVwKxm/C5dkw1oaw1FqIy3qmHDkeGezRLLgoSovsVhuJemQaZucpKutkU8+94+sS7lIVdQwa8lQE9V5oTHE+Q172PPc61x0rqFdjlEu5XBJRd5R6ogVNDR0DFnh40KjpXCJfoeKK9aG03CTDpzkbUmj31jPfYUTtA8fYaYszwPjORa0Mr54z28QC/rRPQqLcg2eVIy73voBNmcAQ7Pz1opqwr5VrB58mal8FVltFoe6wA0WF86FIEjL/P1KZkngJ4edHeISg1ITmbSF7mAFRavKrSmTT3z5939u3PuFgv7/TPtFgP7Lf/ZnDBlpqs0x5lyDNOfvo6O4mdkdX+aVmTXMjHdQb82g2ZPEih7shsRzuVXkJSvrs+N8eOQSgY+ehfIipinT37eLZ6f3stO2QEPtFRpqr3D9++0U3UGKtVWcqThNWT5ETTFIRqR4MN3P0eQGREaBbIRMWQ26N4hUyKGlE/8Xe+8ZJddV5u8+J1bOXdU5Z7VytCTbsi0HCScMBkeMAcPADAzMMIAJg0lD+DPAkEwwBoMxyTbGOciSJVtWzupWq3POoXI68f+hNfaw7l3rXq+71r0ffPfHqjp1Tp391rPPfsPvxeWZpWldD/2Tl5BMlBOVBLJSKQ+u20RWsnjy7IdYlxwCYCJYxvmVBpPDLXyp9it49AKG7iXllZAMG4+dxJQFgmaCBaGUR85+js2J04iCTdEWeVy8hj6rhYIwQrfTYHm+lcZNB6lx9pLXHOSG3URa4nS/VMkh2cNg+TTtIz6WjfiRpDJE5zpijJIojnJd9Uex0Hk9XaBccdPoENmV1tnoAa8oMleYotRVyZCucTQn4rIF8unHwBjDdIBTU/ApYdJ2AMl9Fc0DfyZetp6kq47L5+8nX61TUjFHWBtnz8KH6a/oYcZRTonWh9izGbM4gcPzTgxPF+bkq5hei8plC0wfiWJIMl1tG7ko0MVTobs5VR39O5uonBtFExQWgyX89vC/calxBhmLs5Xl/EfdR+mllavSu5lLV9I17mA+G+MaeZgyMcOIUcrJtWtY8Cm875V5qotxRAQk9zxVGx9iUY1zOulhaz5Kbnoji4kakmKColJAMWWc6SYsMUvz7DkmvNeCoLOq5Seszx5ANUyOLPczWaik4Sd5JvyX0NlQQkXNS9xa6ONkcT1PsBOvKCGte4D0qdtpi1eSlQX8NT9n6ogXVRLQLjTTFrH4aPNhXLLBWMHPY8MrafLPc21FD+KFHdXhwjZWq0eZssOUMIciCJi2A7eU5GCollM9txIWFco9D1AZtGgsLvXzHc/5WSi6WRWaZsH28+PpKzkptvK54BNsUnuJ22F8QpI7Mp8hkJxjdeQ8ZO7hgNvEEvv44OW/Rs8FUV0FJEcWgMyUi9FXOihpdVGIzZNKBzEH2nny0iq+4P8mr9qX8QfxTlrNHmaKZUx5qljRfYztp/ah+6ME5xbIBAMosyPMlNbw8I0fYmNvF/mGea2xAAAgAElEQVRhm0ErhCmALS3JppnNfsQqBV1UuWqhj68/9kX+vPV6xnINtA23kgmc4OGWI2T77ka2bSJKETFskZIcZEsC6DEPTVI/M2YFCTnI9kP7aOg8hORrxIo5EUWDjGnxjL4GDQkL6Q37KxEyLBNHuV3ey0l7OSo2IeYZFZdimPOqk8c3XU3rxAA3T/Tw8c9/6S1z720L/cMvvcCxPfvZ6nySg3oli8pmdGwU0SBW2c3QwDJURcSlLFK19jRm0sFgz1Z802cRkgUkySTakSK6fpb+/otIJqIIvTNQyHLSt5ItwnnsQhq9qFJsa0bHRxYbpy0iCTayXMAwLjwx2jZ2Novg9VIQDDKxBda6x6mtPsfYTCMvHPswt5gRNjjfVHaMK9AXHGbNsa8zUxHgB6vuYm35AR6QPkYGHy4rTU1yiqaBcs60Gkz4vPiMUZJyA3cdP8PmXBcDiyuJBR9FyrqwK0oZTAXxWDphMUzlRb8FYObkbYxlsvgW19J6432ML5Tz9dBXWX3ma+SdHq4/24S3LkhJ9Qm2DoyTKGxClm5GJEkeEcl2c8ZKMjDfT8S1mm0+BelClq5l25zOZngs9iIbJ66kQVqkwR3DI3sBmMsn6JqdJhloRAYuNsYIlDQAoIuDlEkP0a36iGWXtrhpI8+ejIwhpOisfpXVo9fhUE/QVXaKHctep2rIS27yHzFNKBQ0ZgoT9LiKzFQoeMO91EhR/rPho0imyffOfJ0O5SQnynw0juRxWjle9Xp4vdRHg6rxbNKBBvgMB61zbSyYldRbNh+0jvG+TV8kIfu5tquPtokhugNbONVosyPzfVbM6kyPfRpsCVd4AApu6p0vcFiponBhR+lJNuLMVxDYfD+V1adIj60klVMZrzrJerdJriDQM+rFLtVZ5iswPl/BX40k1+i1uOaaeNXsZH2Nie/Ipyhd/RccoXOMvxokM+km1FiBNlNA9UVZ4zlItTjIk4utZAsO1JCAI1mgzFPkBfflJGct2qQIPmE9RvFFsNw43G34zb1MJceQHGtJrQ+yuu0nrDxlEEnleH2xmR2x/5mlDZ8rKcE7dw3v5wXCZFEw6Lcr+fbi9Rz0bcSjZhFNifqcyN0bH8QZHGfopfuYRmJ/cIHLfafYsOxlBMlEEG1Sth+/kGK0WI3bkcdvJVFF/Y3zWabMntlb8B4s4pzrAQxsJYIgRyDfR7H6Iv5w6VayDhe37UthlEzzfH05c4EIsew8sUSKpKeE0nkHx5qdyIaNIQtg29xyYBx33stvtgfxZrO4RxMs6i4EUUCwbPSmALbnzbyX2hmdkVIFR9ci4lgeHzrXyj0csULM2iG2qwPUiiNMWWVMmwE6i1ESkp86YZq7Cz18T9lCWpTx+CzUOpn5WAzZMrnj9Rdw4+Xer/9/7N75f3P8P4G+rmn88V++wOrSvRwM1TKYWkdAs3C4M8yZEk5NAdvGNdHPrMfHn67/EMH0Ij7DxLAt7ur9KcpskdyMG9FpL/l0iwKIBoL5Zmm1HRBx1ntZKLYQcg0QzzfisGSWWZUMOAaJVh3B65vlSNdVOAQHiqyxbt1TKMpSG7Qz81UY+z/OaiFKu0viqJBmb3OA0pTAykya1Rk3573w0bUGmp1Ed1UjYBNkkW/wOcYmSilLNiMsO8Rn+BEt9PCh9O+Ze/0OxFTtG/ejZPlfKVn2PIlEKZ1nr8Tvn2Nl3T4qzoQYiV/NQOESAErXPUyw4TWm4vWEHQnSQ5eQGtlI3dVfR1IKlPf5EIe+gU+YJiWcQ7RuwIPE0b7vUzKRZXDtPbgFLzFJJotKtWzhlwReSyao94apVUVmdIsFw0bFpsklkzcm0UI5ZC2IuxhiytnN0/5Obohvp1yPYmIxKo8QOX0If8dtnMrkqd77WaZWFdnfeDMfKV6FKAg8WnIEWRC5cW4t00qcsObBeQGyAPNynD53mlqtFodVQPR8ni86fQwG5xD+RwzWRkbAwEYgZhgYAsSlpTl3WvCZhQQPpr6EuTJMZ6SZ1aluTvnbEU0bEZt/ef04zqlGROccm5WnWOV5hh9HQxScQTqGmxiwm4mLHi7KCIxGM0yVnsMcXUts+hLk6t8y2XCQi6Im6pLCBE8vuMmZMu+OppAvXKPUo2A26yzO1vNncQKnAR/sNUjXOOnI52hamGdcb+H3s/9MbfsPia6KM64JrIrnKU55+Onkezkgb+BO5cd4+5w4Y9cjGg0IzlcpzM4hKfUIYgCjeJY/XHspD8e/TONMgj9oXySbWE645EGGo/sxRYHrtCKr0zkAFpHxmBa6T2Coxk3BITKiRkgNVjAdL6PJ6yOy+mnip7dyeOoqalMVF8oNgbJ+1C2PsU+/jFccV3G58TJXqi9Sbk0x+FQlYn2WkLOM/JyXSPtJnCENy3Aw13UJ8fNBjKKKWexE9IbQtpuMWbU8WXYdunThQcq28ZIhI/ioSiRpGZXYODjNMxsCdFZGqVgwmA6JgEDFosGcX8ISBHTl7xMSpeIc/qEJKqQSdHGcul4n59e2MxdQ+Odn59At6FQgK1rUSKNstBcYUxwYSh5fvI2rPL8n6Zji/dq9FG0FG1jvPcuBrVej2kXCiTkcPSY3zGs4pBf51+/+5i3z720J/e9/9B/YffV2zGCKOGHG7Vpu3ZdhRd0fKImc4syhFtIZLx5xOw9dVYFo6ViiiKEoGJKMp1jg9sNP45kYgkwOsHFIFuXOJFWxGZ7RYwTHwyDJpJpWY7iL7Fy2n0znTcTSzXjD43gWVjDDIvqKP3NYvIghp0y0OETDQo7xqRZeqZ9nQ89mrrQc1MsqPYzywYZqis1+rt/fx/KpCMWqPLen/HxgPZyN+AilcsT9bm44kuKayK8JNiyVOvSlBF7v+yy71m/Ea6dw2Wm25l/kHdIrFDQfQfc8nXmJ2ZyfZXqYwYFNSLqTASvKKTPIx3IGK9zPcEi7jpqOF/BXH0NLl+KKLLmW0AVKj99IIHUDAiK9sw/jnTgBaQdBMYo530OqvcC65SlSeT8/cKygNvkebLOcK3wqumngkWXOFQc5ZVgcqd3PRYMdbFJXEVIUVCWLIEj8uurX7Hd3Ilo2wWKADeltbCzUY8gj+A93Emz+NCFZRDcXENMZDIeK4IgypYvUOkRMTPYHh/h+9aNo+hirc61UG03E/Rdz7UiKjnw5e8NTXJooQ7FkbCy+VPMTegMlzPrXIsslKDhIiRqGUk1LboQPDv8KpzbHCU89p9VJJsUUVjGGoMZJRT+J7lrBreN/pE/dSHewDocG977UhVJ2P7cZPfyXuoEHK2eoLVRSNfphcmaSD4pemqzyN+y1IGjszy2Q18K8N/oJnl7hJtz9SSK5ap4vOc6GFb/FqWcJGzopv4ppCLw6upWWiRR7jZXsDyT4qvdv3DadAGDGKGfSs8DX1M2stCbxKkl+F3LiN02uy+S4KanxnHglhuKltboTn9Nm8OBHKKaWmnDbtoUh6SiWg5DjKKscRzmQfzfjrjJeWGNjiz7qZ7t5X9V3cPoKRHsMumareKjibtZbp7mi6jkMp4BXMym6lhZMTZdQRPAsyqzrmmLODGBY9cwadciRUb607E5OelYiFXTs0SLiXJ5twnlWde1CENxg5ZGdmzEKh5GcGrGVi3hK83jKc3S/VsrUuJdyARJXh3g6chujVPHf2kyBvEHVrM2d/IbDpVUcMK5k1ufka2ce5A8NlyNgc9/e/Tzpu5G/XBzAlARu6D1H29kok2EHipRCDB1kv9pPiauX5aIf2TdHAZMzeYmRXIT56i9xRU+OzT15bKP0zcXswrCxkFzTWPkK8HXh3Pg0Pzr/QRZCpRhtAYSUTrhzjE8u/xnueCV956/F7+7k01/9+lvm39sS+vf+57d4aN1OHFYBl5DDYenMCjFsUcCbzZJ3OjAlGZeuYdkCd+1JE0uaaM5p+is0ntiwjk2DXdw5tJuL9EN8M3orT6/dyebiQVzjD3I0t5LS4hwrC9W4xTqmYyu4ZT5MS9pgruYZpOhfWXj1Plpd9Ux7RG7e6sEUl4ygPGUSyJnUWgIrEyZTLpFjYYmsOMGYpxzB1hHQEW0n7qLMJYsmuyoULMvGUETUgk7b7nn8psaOqj20mLs5l23k28WPYAVVAs0anlCBYaGRixd3cZX4PA3ZOkLnb2Bf6Dmeir3OpUPXIllLqaKmXaDFqsbWsizaSQTZy+W5Pkrc55BLxhkSNlAyvAOHaxkp5RCLq5/BLI4jZAV6q+s4Ym2mtmeWzyUfZaLYgU9aZKy4iv3pe8jWPEqpVcX2zKUUBI27m75EWkxTv2AxWCJxacFBx+D1WKmlnUbaNUa86tfUFlZRnLwRxbKILn8MMx8gOXIpXlPnhtAzGHYzi3oVLqmWHzSrxM6muVoQiKgKj4pH+KjyI/qcRZyY7ErXkB+uQrIsjral6KqPs1a/mYsXVNoLK6koelFtkcPuFELyu6yKzXF/5c205Cf4ZcW72TEVxmHCz5pVbCxc6T2EZw+SksqQ5BFEMY1kxjHkMpLRz2ApMaryU3x58OcMJ7L8smoBpVDKzyY+TJUeW7rngsFZcYxacRf7Cu1sE1bgsRzsylo4Hf00O+uptH3EsQkLAsPScySlY4ynfLRcfpbnRq7hlvmjbBSXpKx+pl/Lu6RDGJab14qX8R+eBuS6Xy/5ry+42rZkdUbNSiZ88wRNm88szvGiPwDTN3EREY62/5bk6Hp8tgOf2ssdmWFy8cs4nnkPJg4OtGjsWRVFsdN8TP8NbY4zeElj2DKziSj7vFdyVlnFbfbvWMFpfjTrYFYT2FawGAwI7AzolJsOgqkMbUMZngu4qHLb2BUKrysX8xPx06wf66Jicj+nZJ0SzeZrw7v5a8kqZhwtuJKDVMzkUE2ZgOxjMuDkwMo8t1WdpNypczonsdptIQlLHJssinRnZNbGCxjVCoVDHyc704aAgKSkefgqB/2+pUXuS6M/pMFxAMHnQlILS4Wai2FMh41Z8KH4ZpGdaeZ1gRJl6fvzpoBTsBFE+OO8wiHjMgT1PQhnZgipCSKJCrZn/FjY5EQdr6ViqFlE0UA2FYLLn+Tbdbcwo5bgK8a57uxpds81oag5vnrx1xA0L4f2rOPr//XTt8y/tx30v/zJG9h13d2kJB/v+8P9hEKLhHbm+XX2HvzdCpMlTsJ5E1UVOV3qQ07fT+tMjNrElYjmLBOBHkZqPsBsUMajZYlk0vSWVSGZFqYkULU4x1XnTzEerqInFmEiGMOQlp4oZNNGKc4RLA5w9WiSV2NrKLrczPhcfP6VYXLRIAcqg8w6BaacInlZQLBtbEFAMrOYohPRKuJOzmDmQ0TsPJMVZVw2a/Cxp55h3pwnHVqGz1vHtOLkQYo4sSkXhul2Zyjz9dA/fwUt4UHO12xCi5Ryw1iBL57TARNBNHmm4i8EXjxOLONkvNJJvvoKEqqJiY2CREHQuaG4nohhIIpBBEHC0jL8LvYc3VYZd/TtQ75tmKPCCn4mfRYDlcdO/SsLozsZL7xpZwVfF79b9issweJTU7fhyk0Tiz9HY3mKmKHxj2WlnHQo2IJARS7A54cbGE5fRx4fluVgtERCNuJUJJbyq7POMeSZ3TR5eon4Cnx423cRZB8Z0aJ59DD3vKJSiLQTFzKMlz7HvxaOkzVjvDD/bhbFg7za0cVcME0s7mAuqIGg8PC4SWn2n0hZJbiI8NLMs5Qpr9Dqz5M2biRtltPgXQnAOTHBed3k9+vLGY8sxS3kQhrT7kGOL+IrPI5iepit/Qqac6mS0qmPElz8JVek/o1/HZT4feRZKqwASuEgfcV2LHVJdTJkeXiXtonnSDJtOfmQ6OSr5LhGfJBtbKVorcUnfwe3dIBeu5wWYQoBm5lDfoRKqKhJcMahcq9zC/1WDWrwMJKU58HxFAnZ5vORcpzjt7JOn+U5tZpVrfdjCBb9RYmPJJLcmcwwInwKPG7UyG+pHahCVk9wPCrx2uK7cDhWcrYjhZqZZXt+F6GKFDPjq+nJXUaydprrHX/6u//go3GFPeJ7aF94nkGlSEWyGUNdYME5z6qMThkWz/lc+EWLjvx6XqzYSKk5yKrpIxxyJsAGybIJp8EUYcWwzZl6gbRbojSl4JcM+oKtGNY5FLWSLwcHcasmBzIy+zMyy1wmG50G5U6blAm7UwqbBky84/9ERB5ntfdRDpbW8/3Gu9mS6OHi2F/4b/ylJldg5SO4oz2YRQcu1xSaKbIbgw2yAzFew2TcxcD4pWw9d4TK6w9QbLHJ5AS6rQ2sl48jyiaeJxRe8G1hxkhjI7K9LEUuv42M4mNXdSN5I8Tpegd3De9ns7QP4almAtYuvhX9IKMRL/WeTlbE4/yv//y/VEj+P4y3HfS/+u0v8ODGG7ll6jDX//xJFqUChZuKRFfEKe65BhLziFefQfHqiCmYHA7wWKnFgGagSS2o+jg+ewsD9XfjLixpkKi6xl0HDtJTFuS11lVvnCuUy7F9TmLtpM4BweZQq5OET14KClnaUmqWIOFOPoE7tYu85xKqxJtZlbA4Jfdz8bFjmFKAFzcEmS67DEWb4TOnn+Tm/c+Q6PMg2DDQ1MDKjn9DFN4MHlmFJLbiRsfGKakkpQS2UiRQiPLDiod5MXAYG9iZ+TCfHFvDsbDFLzrSfPv0IpFUPVY+Ti7RjTvYjugKMTizn1Me2Owa4Fl3GWUZg2tmS8kXZznt6eOl6iTe7D3YvtPMuuYZjpwl766hseigPtvJXSMtHEh/hANNExTFMUQhTnfoRXbmi9yqJWhPFHHZNhYCSdnLD2rvojo/SUJSebpkM0OeNi5NnCaYsag8085YaI5nNgSw5BiVCwbzfomCNMey848hyRdxun2pCb2iZfFn0iT8Ef74xX9msvomFqJv2rplJRBwgKBSHt3HfHwVuuUhLh5ASB2nTK4lsFiOX0vRtmwHgiST0heRFQm95iSGaxEtM0u6sIZSl0Gi9iUmzt9Ad2Azt44ZqPoCI9b9tJgGecdneDZ8mG6fju6sQK04x5PKPVzP37gzvY/s1Ds4eb6dQMHHonKK2EKKUOQMHZFRXtDXEzVv5hIUFERGGeGrZBiwy2kxk3xFrCJiFuhVf0GFMsRZowljIsKh8h4kK0SsopcnghImArYg4c2KbDsVYaExgalYjIRdbHFqrNJm8ZU4UJwGug3/OaYy41zJKnMrHxpaR3PGwsJERKIgx8m5dBzqDJMrfo6lLmXZ2JbAQvcyYoERHKLI0MBNnKuXmcsdpKqil0ldYbd9CYLvdjTbyfrzR1ms99PnLsWTfplg+mWyaDQ6nAwVLSy0v/v/Vs06ue10A+1d5/Hm33wv4XXzrdtamItNolsZimhs0UvpL/0HBj2VOMhwjfYQHxrZgxa3aC1qTAedjNU6sf0SL8Zl3t2TIZNtp9NfhyYrZNMx9MpjXFI9jCQZ7Ou6kefn1tOY9TGtGExIBmr1I8jeHpyan3uSl9C0dkkvS94bIfaXNPFoLeLGIcwqk8JyG2kBDJeIqFmUfktBzL3p5rEFmPcH6dpSzzn3Mky5hFt3vYzhADnUibzWxPGqi0dW3sZsMEdtMs5/fPcnb5mBbzvol7UF+Ozt/8g7cpcjmiKD+YNULPaxeHsnkunDdCQxbZBHLkX1jZEr7QTRQhjfyjPnbueM/ySh8AFmPLdzz2QligBHnEeptXtomtlG1lvH0y6BWMpgeUanVBL5hpXnkpxC2BRRgZ9dPUDGvwL/7HdQPDeQFDUCCz9n+bDO1adbGKuq4/q9L+LULQRbYP6SLGZrDE9GpSU+wMSLIWbqLX5zuURXVKYxp7CgerksuQ53ziA92cMlY36aKq8nnh/GHVmBLCoUIwt40/UMBX5JPniGZcPfx0j2s6f4Gl9637/hKBT49O5DXFYIoHjKGZPH+F3oAOnhau49ewBvdpoDqy9msjLGRfuepXamQDIKn3pfBz51lGkhj4AMSjMlyTliqTacuodVMxcz75rhqWU/QSJE0RlFQObyQBm1yiRjqRVMUMXB4GpsBELxbpTUd8h7N2JJEZTCeWTTR85bj5I7S9OAxsZBLyc61tLTUEsiUAOiAzV/ElOOYao1RAuHuE37L+z5Cn5X/0U+9PAfuPbQYc42bmIq4ECQYsjOjYiCtKRSeUGpct7VR0m+mZy2H4dQjaQsBbyDkkC5msRRuR+j5XUM7yyWKSAIIFzQ8RF0J7ZSwDe1EevcBmJiC0l/P5Kaw5YLuNJ1uJL1jK/9AblgDz8qfI/zzhJ+nP4iucACT0x9muPhCixcXNSbJzQ3znxkgtc8G2kcyvFDgpxjhkXxAKN6Oa9JpUxZJTSLEr/Aw15d43jgeZocfh4PvMqca2bpumyB1iknonUd+zfuZNXYCZrGewhMJ5jbEOPJ2vdiCyI32I+ztfAnTuRFNoSiPJz9Cqe9JQC4dRNfcQZTDvODI7/DEndglPWgNjxA3vLReOIeRFtiru0RdP84omkjaALTssBfp2J0C2k2jl1DRL+KtH+I8plK/rq5lOmgitPOsU7bzbzaSA8tVOd2Me66El9xgh1Tf+ZT0y+R9StM9gUID8p4+y0WY17GmksYd9XRU9fAe598lmhqkX/69NcYqKrixsk/8vP+X3HaX8+/Rz9LoejiXx//IQ+03UiDe4qUFWVKCPE+3+M01p8lEXPw9ILCpZgEIkty0PNplRKfxrwm8qe4Sm86hjtTRiHUQ3HxYmTnOJK3j8bEcpanmrlk/d8oJispnFhFxwtPoldbjN3jIztwKUcXxzHoZLisDr08yyfD4yTmQ/xp+iMUnQtcI/6OMhmctptEnZfWFyYJPCVjY5O+SiBzgwYSSFMi4qgL3V9gf8/F3PejX79lBr7toA/w6e98Gv94lNtcm3CLS0/IC+X7mV/xK3RdRTt9OysSJfjtWTILKWZbO0mt6SfacwuhkR1vBGGyYoG/RJ6jtW0XEVeesjMfZWG6jf3RIWqks1SleynRF+nymfyo/Er0bJLbTt9KwjXDMxVpjPBf0BQn/mIdrUMH+cQzJi4NJAvcpQXK1ycZPhbCnFGZqhZIeU18CxLBhM0nPiphOEV+PDFLfcHk3uoglQUnUdPmoRIFHYOOER+f/mucgiriy0sgKgTW34MSXY5pLiDiJ9H5ZXKpNHZe5WxTK+3DA0RSSwE/UwDpwrRnHBJDLTIBv8LJ2kuRkh6ElJf1XftJ+ny8vL6KtXmD1YNHmPKsZ8S3A4ulzAgbk5LxH3PWXcJflt3Axy56iKeU93Be7HhjTiQzQfXCT9lyLk9Fc4aBokFrvArDVlCH52nvLjAfKXDY1UZ1cY5Bfx3dpcuYMiqQal7FUyUz4luSmm0yjvBl6btohoRL1pnSnHwrvZ1PPDbPttMnKUoiZ6uijLZfg7fQhsySu0XR0mw+fB9HLvociYiLzlIXm8SHsTp1BEGjekcfrnCefMLBsd6NvFh9N9G0xHWzr+CUXsOvraGuSmeh9nmQdWxLeGNB+O9hGyqCrCGdvYue7Hbu2+xFMm1MacmmWuxuAHqF9r877j1PP0WNvoKCbwDLWsSUFQRJ4KwRYjrUxYcXruVyO0RaShMy/Uwqszxh9LBv2UoMTUOwBEaa6nGaeYqCA1sUcVtpdMFBuTZOPB4mXRYkkM3h13JMBwMots77Z15m1fQw99XfTtrlwJBNbEHkeu1+rnecJp3UaejME7LqUQpfQrBdmN4DyMKD3FTuoHDBtbnGYfBe1cXka/ei50sQ3HOUXPQzJmcCrDBHSVVlyHlFnpNuYbf8LhzZI3jif8R0NHOLKXHbo7vgnILpt8kth0NaLb+57uNMlS71dLj39P1c+7u95C0Hv7juZq7te45w4yK5LRaGIpI6X8bP+u5gTgnRlhumO9SCYDkoiDot8jA7VjxDe3QQzYInEipVqsUmj8GzSYXds3WYuXpU30lsNYuZr0RyTaAKNjv9Bpf7deyigNSr0Df5j6zb+whSPk/v9RWU1fahNy3ZwP6kkycSCpZgsdOzhqsj+5k1oiQIUi5PMWv6+L30j/QKy7jOfoKyzj2UluRZVhZnbrIebWwblZsewrageKCc/VMlfOtnf3vL/HtbQn/33uf54dwkIzP1lOfmUDNuzmmwo34XgXmb2+NX4hGdxM3jROVV5DofYG57J4XVNo7hKBysZtAd5FT9MTpiFnVlGZK6TEAxsG0Ij+QpnXAg2yG+ERE568tx+ZCNY9RNhdUMjcsxsj7cZ0eQfAdo0OOoEwJmHj57t8SaxXJWFDQCZRkGS2WKh9KsP2ojenwMVP8Lmj1Azcx5cv4WvN4+yo/1ojn8nF75T4gOm+2Rf+e3JTncRg3ThQivBDPUJSe5vHcFBTnIjlwZfk8t+uQx+rPdlM/PIdg2kmnQX1PL6ze04/HlKJ+foUwYwZIM7JCNt7KAeCEQlkiUkhi+iGL/NdiWgmAttV+0LyyikYUTTHr2cMmpKVyawWwoRPnCHK+u3sDpD1dwE4/y19wyCrbICq9MrT2InxQTY40MD28BQLBNRMvGlN50XTWPdmG6JwlvX8RraDieduGYsRBcJo9ftoMTKzv4J/t7TGoWugWiAI0Oi9N5iYcS7axe3MK7n91Hw8QY933in8nUuzGSpVRMudh6roBS9zyNzc+gBQRGxDqa6UU3ZWTBwCqKHOveyT7vNrrra9h8vkB/hRPNmeQDPEBCDlN7phxjog1//XFEuUB2ohUxI1ExegC7vJ/iZTrJ5GoWT72Xl8M6p+s9WLKIYs1SIx3HmIqhIBOuztMga7TH9vBN+98pTWtccVrjSIWPiVCaEmkBVRexUoeYVfYR1gJ8Zeo++vxunvDkGK8ME3eI2JaFaIMpCWzXd3GT+id+xceotsY4LG4ma4T4yb4U7YaTp6ocHI1IxBUBn3yemwI/IKQnQIFswYNoWyRdQf6LzzAmLO2AnNlDbJn8MZJmMujyc//IxbAJDzwAACAASURBVESK7yCX6eM9635KaQIu7hZYOaIQkHIUPupGK4TxlAwT+pWEdc6Lt5jjeGsHX/vYx4kWj1BM5hivfAeIKu9/5jHueu6viLbNMzsv5ZGd76JKHqKg++hUO/jQ+C9ZV34Iv5hEnoPwjxSUhTddJrmQg4IpE05lMQSRaU+IqswCpgidzRUMOCoZcdYy6orSsHaAnnglI3YeUU4iFEuR0lG21Z9hR91ubCnPdNFJnWrQ311FXfMUiiCSeylCw8FZ1ISN4QM5DV1XraAzsoythw8Qy40ytrOMiclWJrLT5JQ8ifJtnFuznFFvBYagoBo6lmVjSTqKNkDRtZL32o9QziTHFhoQz06Td3RSGWzjROl78KU0Lj3yPF/5+S/eMv/eltAHuOP+++ir3sSotwIhuYg8nieam6Kh3MTIiMROT6AI/dw4U8NYbA1O4wlanUdJ7bCwnRB8RELfYJJtg0C3TXgvHF2vsNBh0eyyeCquMpIKUuONc1PJUuGI2iugV9jYS7VHaOkYqm9JKc82ZIr9y/itOU+3P0FMtri3rID43/arASrYlkhi6GLmO29EFPMgiujZEkBA1ZJYkoQkW6zxPEml2kXCLOdkdgcDso+Ee4pwroajNY9RNdlJ21gzpUmDgkuk+6py6up7qVSmcYjGG/cpa6kYtk7SFOgviPTmnFwf30y49jAud4qBeAT5SJi1QzM8VnEjc+UbGffN8YVf/4BwpsjBNoEXNwj0Vyj8c9GgUS+QaQLFYXM2J7Gvv4RrUzoOy8lInYBrfAXKjEB793kC+QUyq/IYfifdVUHEsUYWXNUs6+qiefIsdkHEodlkShVIiHi0AsMfV3E2ZBFMETtTgujKYqh5JNEibYJPgrTuwr1PRVmVwora2AacmFxHe2gSt2+KVKGUWYefJqGPV2cvJeqwcS866J67gufam9Alkw/tncObcaELGX5+XYC1p2DzmIGIgKqdp2LseeI+Nz6tmf7YKpxqBEduGkPxU5QdZLQX2b1iP46ZdYxELyebdSLkQXYl8ble5xvPHcFttTN1YyXHV+o8Ir9vyYYsHVEwMBERAE1wcLG1h6IOJ5RtmKKEbBhs7e0lWmayOfAAQXEeCwmPaVB56uPkgwNYQgF1fgN2ugHPdB9GvJ/nynrpqoxy5yuTlCz0ceKaar4nfgDZYXB3xx8IFDI0PZrElm0eWbaDEx1tDMXWImkTNPb/hg++2Itkm7ibrqXR/04+X/lTvvLAOdxFkbwqMRlVKS9fwGi3cHYKuI6IzPgC/OSWOzi+fOOb8ha2jWrolCQXufrga9SPvsbxjis5vPJKsi6RnFNBwuRq+zneI/wR77zIXtfFZF0SHYl9CLMV/Na+iYReTshZxJvNIk7meOfRl1k72790CqAoyeTdKl1tVXy38i40nESLc1QVxsg4PJRnZxHb4H1rHuX8bDt9qRrKxBla1D4CVVkKCZX5R2OsOT1HUZaZ9zux1AD9tZewZ/1FFLwp1gz3UDFwlv5KCyQYrb6C03WryatOvPksrWNJwvkJztXUkVEdvPup3zERHuCVS+5Ac/89l93pLnK+DuTiOB0Twyw/cYbv/fT/D+T+3x6WZfHLz1/D4cr3U+oIs27xZb5TdgXj0VJwy4gzeZSzCQTTZo0mMSVZbMm9yO3OveQuzaH7LTDA/5SEZ99Sla2lCUzX2WQ/YOKK2ljWUiawo0sklFWY3lRA1W06OlNk/TLjJX6smQoWxldhtg3grzwPQKbgZlp3U+NZ4ORxlSuyjcxVlpLOxChRTyJ19P79bzFUMvEaMuNOaqenmHVvZHb+OmxLwld5Arcyg+VOIAfjKM44hcUmdhcSzLh7uNsux10/jCiZ5HIB5meb0GeWkUpU8Frr/QxKBggBmoV6tg85cE/vIGdFONF4P5vDFvX1p9HiPo4G1zAzXsoO515GxjbgTyoUhARS2xE0fxG/DGWqhTkl4JkGcUogu8PEnvYSf7GJxXCI8JZ+ItFx9HkHC7sr8V47g9e7FCA0bTiVkolko5i5SgKZWWLGOK+FQkjnnaxqXcBVWQAXiIcUJg9U80j1TrZb/dTuPEjIn8KwlkTbHBcKm+wieJ4Syb3TAgWsSYWBqXdgDV2DhY3kG0ePx5BEL/NeCOZsRMsmqyRRESjmRvArq7DsLKLgwRE/i8/oont5OYJts+zcOV4Vm3m+tY021zSXTlRTOR+nte9RPLmZN+bPEEVeXrGJ0656TFNkmd7PO08d4ulV1QTdTSjFGgTPMSbX+2lvPomadjCy5158q/7M3ro2nhVuRLE1tpj7uSL7MhX+McgLuF1ZHOer8fQ7mHIZuCZaKSxmaVxMcGbb7eTlCIVZkaJtcarR5Ei7xOX7D/Bqex9V6TrS2Awqy5D1aQqxjahn45RmxnjX2BG2DXTiKeS578aPcPSSizCdCjtf28MNrz2DJHv4/Ke+zpxT5Kopna+eLaBZKcacFqfCbnzJBVa/9AAjfovvvv9TjMeqaRgf4fMP3U9vTQMPXfdunJqGqmsMVNf9na0rhk4ol2bR68MQFQTbwhZEJKuIWxsgZ8Uw3SVvfF5KFrBcCrYqIeZ0rnviKdZ6QVmYoEE9SWg+h6NHJFsnYKZlJmIe5PemcIaLpCbq8VdMUcyWkE1G0G2ThVdNLN3GV5UmM+lka9cs3tJ1vL5yNT/c1Mp8eEnWQzRNEECyLJpnxtg43M2R+mWcq6inJDHE1s5j3LxrN1WzSYZjAVLRStz5AhUTYzg1nVMNAvPh5cxWNDMfzNFdsZremlVUz48gJv8XlqlyxYkw3/nF42+ZfW9b6ANMTU7yjd98iSFquMGEy3OtfLsjyvNVF4xGtxATRUKzM7jzaRbjftzFHC1mP+tXnGH7o914R01+d/VlJHJObpt6hVhfEV0Au9Qmv8XEDNu4/xwhsPXfIbobIeHCyjfzuvUyhm2xae9J1JhJ5WXzvGLeSqZUJdS0B8mRY9fgdhq943D0doxciEhhD8tKL8eo34vhSDJdkJBq96MoBWxbRpTeLEUXcgKWJSN433zNXpDQcipqub4UvBQNbFNhfmwd2vgGcvPl+MQ5ioZOwepA9HVypP4XfGAmSjG5nb7CJRjuWcZrF9nJE/zK+07eGfwTft8cpiDilJaE1xYXKpmJV9HcsDQ/ck7EtGSOTLSTGle5vr+LXCbC7JUeKtZ08T+Hq1chUwWSW0c3JP5w+F0Uc262NL5OW90gNjbKBT95vujG5Viq9rRsECxQX1IQdnsJ57KMh7w8s1FgsMJHdcMM9c6luos5A3YEDCThwnGAnnJx6tROqgfHqe/NMBtdzvFmN24jRPnkPjac68SUvZxreweDTW50Rx4lO0coWY4tROjoepXxigL97StQnBniWS9eWWTBYXPNmkdxmjpS0UI9LZIYkzH6A7TMJkl7vRSRKckklhqpiyKSZVFYZtH//ijJRCOFgoeDmW6uejXD+LZ1XPr8KUythYH66zHDkDBDuOUF6i96AMmZYm6yg4B3gbn+y5hMuygdeZzWkSkWAx4qF0x+9c7bGGmIcsP+SiTfYarMPKO5KzjRoHKiI8+0K4x9QfRLMnRMWUE0UwQHf0V+/iYqFx24tDQfOP0Ia2b6SLo9/PQ9d7Jr07Y3mt37ChrXjmb5U0uIq7oHiegif11WgyYvrbhXTGuc98K0W+bO55/g5t1P8eJaCX+2SPWiSuW8TjoQ5dkrrqavqm4pddku0j4zg1srMIeXiVAJZzy1iGYGzWMjBkqQbJvliU5uif6efZNOpq0iWxwKSe8KHg7ewabkPD887MXA5Kh6nlleJOkv4ZWyd7N1OsO7Xvgzs+/uJuuvwx8ep5B1c2JiBdfOXUVEj2LrM8QXewjGtjCTPc90uIqzlWX8qlElqNvcNZDHl5yjPB5nRknwvfVuFsPrUDWNosPNjUePc9OMjuFcaiKT1mcYVjMUJHChIuXTlE6MMR8JkQxH6PP3UZovxa/7mfO48cWHcc0bmIKALSzw9Z8/9pa597aGPsCRI0f427PPc07xUJgQqRLjrG6boid4JfNiFa+XOqhYGOPmJx9CbyxjUvdiaSIR1eRgcQNf2PcTqvzzzK4p4ZvmzewceoXWuTR+XUATs0z7HQSyNtWGgueyL2BbBqLixpg6TfLEA4DNa23NzMd2MCTXsbYooAo2sidOMRcCW0bAJrzxF5SVn0BcEDErLLAkCtPrOGTKML6NLZkqKuUCQdNLyj/AfMUBLClL2fQW9HiYw1NPk84U0UUJuSlER9sICcPL8ws+tpvH8KTbmQqc56juZtAHK+duoGN6G5ZgINoylljgfOleVnj+xp8X7mUyVkZxxsKNxjZ1gAoljssTJxyaprb2DLYNi4uV9PVuRtddb9zvgi0vycqKAoqmEVb78ZQlCAhZMAQaFpM8YLyD8pZBDk+vpXe+Cb8rxWwutiRtgUjEuUizMEebnWJQFonFJhhOlHAm2Y5muQGBd/Yd4h86nwJgNiDwn++o4rx4NUHfKdYnJXLlo5RK0CIp+D0Fes5fjKSZaJKLusEhNhw9injB5m3g9fUbSUf85Lx+BMvENzdGqrQOQ1kKVouGjiUrRCKjLDcO4h4xOevaxLijEaeZZZnrNQYcNdiBLC3lE0xNNmBMlDDDUnNrZyGP6RAxBYmVPecpbY9A6wyFYD+Wkgcgrwv8JruFgayTT/a2s+l4H4vxKf502Sz7WlOUpmtZO3E1sWwjB9o8XDIwgZIrQ0AgryTQS55lmTXEH+072boQQjZ9tAUTBKW/8bi2g/J0BYs+m7GYRtXcAqFMOYIlcLpepShZ+IsG9bMazqK6dD3uIZZ3PopiaBy66CIWfQGGSsqJ42ZyQkHUTNzrXEyEyxEti1WjvWw4f5bTLas5VdNAY8bkE+dzxIaP0xcSmHanCZk+ZkhjCTYGOtVjUzhTBfa0tFIr23SbpSi2SaUZxy8VMAWRgqAgizay8H/CKBuWmVU4bZXna6M80VzOmrk0V87pRIsuHq4qcDYaIlawmHWKtCYNmga6GK+s410zKldMF3HZEnP5MVLJQbSyDpKRUqqnxvjA1c0sXtg2doyM8x+7T+IVFByBejI+lahVQsKY4tTCUb5183u4blLj4wM2AmDZS8p3oiARF9LkhDSV1pItmFhoGKSFHDPMcV6eZcGe4ETwNeZ9FnfsihByKpwPxPjmT3//lpn3toc+QDwe59y5c3QOneFHyadwj72XvO2hsjhPU9U0j697F4pepHxmnNVdh2kd6QLrgmiYKbF2bJKKZIZZp5+/dewkoAapmu5GMQssRF3I1iJljmpsOcy8VqTeGWZleB2Fs3/htKIz7JhEEH1IjtWAjeRYjSDIJEWDKdnmqGqyIFncFNnP5SXPMN5Txe7gdo6mWjHtNxX6FEuj2kxyZzFH3h1ml+Djf7f35lGSXXed5+e+/cW+5V6ZVVn7JqlKiy1Zi/HG2DJgN1v7wDCebhqYPg0D3cNp8PRMD8Ppc4Ae8Jmm28PAgLtpug802BjbGGNbtmyhfSmpVKolqyqrMiv3zMjYI95+7/wRqaqSUMmSLVO4Kj7nxImIFy/eu7/3e+/77vvd5TcW1vlH5gijmsGCsYqNi68S6vomrvVJvpCr8lDe5d6ex2Tb4e6oQ82O+bfFEsPtg0zXDjNhnuKBaJ3/J/phnlJjxFfNCpiTPXJBmx2GRDg+C3qKf3n/b7LZK/Bnx3+AmIROXKAbDWPobd5jLGIoxbFkjF/ld7ndmAXgtJxkRk3xyfj9nFLb+Qn9S/y4/lV2iHVeVDuYldt4IdnJcbWbVTWMITx+wD5NhI0S/QuvrnReFBpFPabqLDF9PoPVyfE/nv4i6dDjv9z5IFbRwMpfaRgu1mqMLK/Q1FzecfIYLx08yMyhg9R8m+RSh4X0MLlKwm67RV06eMri0WgHPWWxvbPKtt4ad996Es0yKVcuMbLgkfubA9Qyw3wjfYFspNOZnAbdQL/sq/5kPkJIpoYuQaqO72XRpCA5l2W90B+ZO+J3OHjsaYrJGp19Ev9tCjWlaD9mcOqCzaEli6nlLi/tyZIxHE5tVzC0m6noo3zs7jyTbY/vPf4VHG8ItzuBGWcJrTpmmAME7dw5gtQazewof733APsXLXatREyv99t0LowYdF2Nw3MhAoUUMQhJJzOHHZSxgxJju79BevQkJW8b8fy7WZEJnx51SMsXOdWusNAdZ3yqyhHneca0DfxemXdZCWL+fhZUjduTaUoq/YppCarEBCJkxp3nsdQ5zhqrrPnD5J1TvOcZnQ8fX2StCE/clqIzdJj3r06zFG3yR8N7yfsdho1hqoZN7Fb5WDTMVLg10hn49d1dPrsjj9T7FRE7UfzTcwGNS8t8sZKifcswkS4Y9hVLKQ03TDDiiHbqyjxNAIV2k66b5iee+izpwgxlf5yNjkOCg92tU1mdY9g5yMHSu3CFS0DMJbHOQrxOo3WGqDEPwLC9jXtGPgxKsb78CIFl45dGSOwyFWUz3s82zflmncbml3n43h6xt8F7vnaRF6bv4d/87h+8ab0biP6reHblSR557m+YPdHkmegApuzxgZ3HeSR+B5eGJmhk8tw38wLfc/IhZt01Zos9FoY7PHjiw7zzxBrZ1kUCI8LwOuSDLr/wzp9jtTDCu4SOFTgcCgzGdMFhV0cAQghqUY2XNr9OJ96kEzVQaDhGmduKd7Ejc4hLJHxceTwrJJaMCTWDNPCg0sksf4pKu8nxwn7W3BRnMvsI9P4c/am4i6e7WMB7FRxUDrckJnlNUNQFm0h+W9ZZMFocDTWO9CCjxfxVxuOYliFtrHNIu8DRVo3VjsNfFt7NqlZif+ccRavCsq4zr+cwVIymJI70eV/tRbJFkzDeiRlPUsvCQzmF1w4AQU742MRsqP7gsqPaOdbJs6IqJOjoJNxmLDEbj3OADX7X+hXyWhupbBQuiSoD/X7U69h8VTvEQXWORAj+mndxdXYqofprKvqxVaVroBSV80vsWF0gUAZf23GEk8XtLOij/NzpPyPZlsPcEVHzRkEohFAoadA2FSeCEUaTGtu9ZdrC4pbDJ9ixfQ4Sje6F23hs6BRf6WiM+KOkpMOa2OB9T04zbo+xNJJjp9cmZx6gqYVsJ42bpHCEi2P61J05LvVW2VBLFHpzWHNjnNu7Hz2O2Xn8CSzpk3VyqPctwS0x2c/oyMd0vJEco/NdUKp/DI7+IHe5aWadS3zigR/A1FNsr1fxtYS7LqYobtjolseFyiIXR1w6tsMdl2bIu1Wa3iiB4TBhNUgruJBNMFdsdKWj6T57Dn6DfK6Kd/57YXMH8/VhUmZI5Z4/IG11UJFLauXt9JwVxNB5hGjzqRd/nGe6e2nE2ct+mcgskzE7rPeGmbA6ZGOHSlDGkyaIgB9SKVpK4ygGKSEIlOLnzCXC/BcZjtIcbB1CGAmJtcq7/NuZlqNIGdPszDKbLbApiqAkaST3iRS/LdtUNZ37lM5/oMlE9Dy7u6t4WoHq6Dgb/iRLmJTMFWRxiT2d3fyTx59gxdrka3e9g8gwmVpdJtNu40QhG+UKn/yBH2Xs4gkOX9wkr7doygxRAk1jnXFVRCgLN+5yuF1llxqn2nmeZ0fKfFr7XsysYGyoyVhmmVZYoW6NcddTD9PoaSzZEyw7Y3hG/6b0QPcivxhlKBV2vUKnXkqd5suLj/Px3/tPb1rjBqJ/DZ566imOHTvG7bffzrMvfIN6Z4FcEvL56fdyorKHd9SqnNfzjHZjxhae5VJY5fBamWnPZsEZZp2Yf/E3v0Y37fLJ/R/kklvi37zwSUbcFsmRiE/veAf31X4EO5aMxaXLNZ0ERS/xyGguCsmJ9rPMdk9yJPs25jL7eI6YSanY313ltsw0a6t/Q3zqL3F9j64J85VbmCkeYqO8nZHeMsP1Kn+x7RAzmQJKCFwt5Gj5NKuNbcyFZaSAbWgsIdmDRgBcQnKP0ljEZxEDKTR0lZAInR/YfJx7bEUhyuDqGWoq4o/T05wXip9pHKM8ci//7+Ei54oWH/7yed7eNCmnSwRaRGT0J+vaqVsskfCbImIJSQJM6Dq/iM1KKmGs53E0yWKg08GjI6qMqsnX8JIkUvOYov9YPGc8T5sUu+J9rGurXNI6VLTjbIom67KA0fGR3YSJSo8/j+9FVyV+Rv8rDhjPcyk6RCQzjBurFA3BJXkXz5lZOtlFxioXcCfOsPVAcRm3tptU7TDZzUns5lEQ84SiiyUPb5Wuh04DxTg9AlwslPLR1L/m2RrMtisgJJGVYAZXps1eGOoxUjcoRCnWDtxG2VvGX6mxz1nig+OneW7PMCu5PCJuMubBofkqa+40zbMBqhpjGALj+f759NSh23j6lju4dWmdyK/jOWmOHdjOtoPzWN0QdyZhR3qZuhgl7roYRkCqVEMpgSYk1doEfmgzVFrEcXtsNMfxGxXUy08tSmAFJRxvBCsov6LG3tZjnnYSXjIkoQBX9ylvPeGgBwzbTTYSG6GH7IgEY+0hMn6GYmwiRYKpdLK64K60jgasRJIRU+Bq4vJ+pFI8kXRYMwzuxSSHTlMEWFpIKcnx5/Z5Xqh63HP+aYZal/j4nT/MYmoSedmZCToJH6l9DacQMzvk4Rs+26ou95xZIfSWiaXFeC/NgqXzf9/yj0mFEZ2CQTMpIYCs8JnUGpS0Hs9F2/CwLh+DrHaRW3tP85FnT7Kz1aV7j82l+/dCCuZeeg8vJDkuRC7Lsv+fktbmgeQlisYm1dU8Xy7fRaA5HERnGkFBtHivFiKMTR7unOP//K1//6a1bSD6b5DN+ia/8el/z90rD3Fu8i5+e/LH2FbfYCVXxkwifuzss5wfPcT/cvJLzC3Nc9wpMNvexT9//r+RifpJwFtmCl1I3Dhg8Y5Rfmn0p/jgyovcV5ujqKWI0g7kJijIDKG3ijH7BFp7Falp1LI2o56Fnhkhbi0iwh7WO38aK3sY76nfIdk4jdQUiaOhewqlC/TUCHgt9Nw4ydAhnt5/P18VCU8ojZzRY5+m+LGwzBFsHiXi/8BjTEX8E5lwFxVMPSHC4GliHpMe+zSTH6FfA1FKoYjRhInaSrqB6j+5BCriGyMODVvjP23X+eiJBXatV7nN3I3QdGqWRimCSIApFT6QhssXslKKM6rHht7hqEjhSIfP02MOi5zospc12sqmKIc5ItKsS4GedBixFAKfrP5HlIynqUYfI5RHSelfwNVeIJR7CNU+AtmfKsPgHIao0VO7sbSzxPLWrZIARGi0kfQzcUV2nW75BTy9y+bqLoxgmOkki9a4QDr3KOn0Ju3kx4EYLbmIbqwTx3tJVJGc9ac839tOOxhnpX2eRtjvpnt3ZZ5OYpMkGnnb51x6N6KZolpvMOK0iMpFXkjdSdHYynyiJE67SZgpILUreXeHhi4wNn6WVKpFGDoopVE5p8gFNTZ3a6hQoJ2zoe4w5+/n4vguXp5h8mUcvY3hhvh+Bhn1w19SaKTTdeLY3tqujqYkWd2jZUO2F0Ocp6VroEn0WECisxFX6MTj7InBNFtoQY6NtEXHtgnciIwXsxQqiqLJJaAc2RxJQpTZIy9ddmR9Nr00HRFgr38ZOTXK3vjteFLxmHmOniywmYwjIhdLb7K/MUTHafFkroapx/zI1NcpTj4LzQqXtBpRJKiYeZRbYzVRrLSzfLU2DZ7Hzz+0wdSaYji3m3j9FFFlB8mud/JMPmY93WZ4bY3A0si2O+w5f5F2bPH7t3yARiHFe9RxEqtE7Ka2zltJIntk2jbltQYbrZDP7nyAtXQJoSS3NF+k6yTIcITQzmC5CXgJE8019m7Mc+/Si4wrgS87LG7fiZMaxbQmeTbYoOUKNj2HL029jVg3OFqf5+2ZC/zyb/3mm9aygei/SaRMCL7wv2E/9ztoKGbdbXz/kU9QswoAHG6f4321x1m3ylwKK6y0cnx/9wnK6xoPmXdwFoufO/Zn7G8skO120ZWkaaVZzAxhqIS8bGNnAjqxy8r2HDMH5nnG1QhNxcceMbHvTpAjBs0vTZF4w7xt7P3o7jCeeB4vXcCJ8+iqA700tl5+bRtQNE2NTKxomPD54RjVuMSHZusUi3sRUiEMG2FclcpRKYh9pN9Ec/II80rjrIp6yDjsLxdXhPtlYmLQNUzZrx12dGgZDTLOAs3SMQxTgJ+i0W2QcdPYukN78gni1Hp/QhKpg5YQSANbj0BqaImDHqaxmzsII53w1EeYaaf6oRwtwaFJpFK8O3ceiyMIoaGURBFhiCqKFIpiv6xI+recBDC4PCjiMgmW/ldU9N/ns9EH+DjvokiPW/QNHuQc9xpfZFncxlPBA3zA+I84WgelLHrJfURqJ7pYQ6EwRJ12tE4taOOzlzXze3E7o0xlPDztz9llP4otIr7uH+J31Y9iRAdoZDSWZIeSbLIvWaTiROiBj2rWaRSHceweDhmUeqWIT08/R7G0xPp6herqLfjRlfDK6NA5Cic7pJoRY5UNPNfgqHmO+XKaXCei+9kCqq2IbQdv91Hs21Kk/SNk1Vls40lcsYSjVZHKJcEiVIJn5Nt5XD9EuNWYWlJ1Aiy6Io0hBZn6IcyoRKJ7hFYdP7VKbHZe91pzpYl3VXIUAEsIQqU4rOfZFdfAfojaI9Ocm/4xEpW6vJ6jrTM++Rms4llCvUgSunSMFrmxHkaqiZQGRjuPKFYh0XAuFTFO1zGqgnljLy9uu5NcUkNGKfQgoJNOk+gauraCbaYJpUsc29h2h7HULON/2UJPFI/edx9KCBCCUqNNzktYSxksRxn+yr0NDcltxjn2mT76VS7TkoTKRhVdJqyOjqK0Vz1WApavY0QZlGcSbq5jTUf80q//2usew9diIPrfClLC+YcgCSHqcVqleEYMUfaW+ZnuFApBLvJo6zbxVaNJX822tXX2LV/idnmKmdIYT5Vvo2oVUZ2E7LkNghao/rEz5AAAIABJREFUvMX+wjy6FTGr70UECWXV5ML0bpSls2txgf/pdIP7km3UHIPniwaZKCHWdZ7LKVwpWMoYPPDQf+O+E88zP26QcgqMjv84dKtET3wCon63x5mpaX7nh/57iq0m75pZYm9YxvBbLA/vR6ZLVJbn6XSq9JwhstkK+aSL6K2Rq5/DTTq0p3KE6JTXJYZdQnOL6MVptFQJJWOkEaPLKw1i3fwM7dGn0OM0QXaeXvk0aqvbqd2aIrt2J05rmlTtAG1jhagwi56kIHHItPdgSJfE6NIcf4zmxMPE1f2AIJu4rF14D3ktwh07Traxj1S3P4I0UYpAC1kzapxNPcPBaIXxaBRPOAQyyxljkWc10PQC3Ywgp42wMyjx/uo26tazHBa/2g9PbBEkGl/V3s8n9v8kHX2TDz5xgg83czilI2iGi1TxKybDA/BFQiNSdGLBRan4610WsaHxwGaDdrBIK5thfrTC+VyepYJGprPCUG2DA6fWOLc7T6a6xvRslRGviqFiNpxhnFRA7ELL0nCsIqXLTywgohCzvo5ZiJmYOkv9hRRew+13g0RDIF9RvkIvYvfqBmk/Ih1dGajXTg+h7foe0tkxzIziv1gbfPrue2llshRaDXYsL3PX2Rc5OnuGk7ceRuoG+07McGHvDnqpFNl2m0axf6M1w4R9Z5YwIp3Q9ik0VigETRaGJvui6eTpjUziOmXywmVNv8hj+VEOiDGs+hnW9ASTiLfzPPtrM8y093DOPIgSgmyrR6N0B7FWxohyV0JBhBSbD9GrGFgTPiNDZxjazNAONmiPBSz4+/D8LJ1OhVJpkQMHv4HRkehdjSDncvbSUer1MfLpTXQPluISqbFl7t71OL2VErlVxUV9jKe9W9kVt+jJHIkysaweYZhCINGjmNi0qNSqTKXPUp0co718FD9IEVoNpOaT6qSxor0okRAbHRSSDhoivYjUYjQtRo9c0rbHv/jXv/JGVevK+TAQ/beWVpxgawJb02i2Wvzlp/6E8888iZmGqXGPeWM7894kDdlmc8ddnB0uEW0Nuz1U3cAMNpivjNMxUmTjHjW7cHnbWpIgt7I0ZTptfnblj/nSyH2cTO8mESY7F+e45fwZLo5P8n2PfY37jz3NF3fez8KOMTJJj9tPnmB7cwWFwEoifDdNvTxFNgoYK99CsOc91LSQP9um8ee7y+gKhgPFYqpf69hWb/GTjx7jznASF4Nk/kvEyQzP3XIL39i3ByzF9536LFOPbJAu30NzwmausJvCOY+9J/5jPwikGSSuhn7n+8jmP4jQtjKNKcViGBOuPYPtHaPQ0HAPfBjNyaNkhDDTiK0sR0pJ4sVnSGqz6OW9GBNHkUaP2GwhYo3AmUMnS6rTj60nsk6r8AjVo19m5PkfJNN8FyIJmTXXeVq+gONv4o6l6a3lkfERrLDQF8TSHEOVOZyhGdKNPexbeZA17SL5IEMYe7TpMCLGMJziK84BpSS1xgkaq49SmXkR3coQ2S5BNouWHSad2oGV24GW34aumXTjJo/b5/i12+ZA1YnsPWBNUur+NYl3hmSrex+AwgRikCZpfwf7TIt35jawNY+q2SBnRyTJPlaWjpDpegSNhEfErUjVYUdtnvXsEJd27mJlxzSHZ44xXF2hWh4h3W0TZ4cYb/nsmnkS0evnu3XCmELPJxVETNbapMNX1rz7ZbrSfC6B9tAkZmcNM5KYccz50QqzBw4S2zbbowZkdlIQ92CsPczoE5+99sWkKZx8hJ+YxImGoUlmx8fZcHI0csM0hsYQJpfHBuhRhDAgFlfaR/KJz53JLGsqxUlrGnV17hKpYSSS+OXkWRoktsFkEnO3LOOoPAvDD+N1JjE1Rc7dJNfZRbh6lGqkiFUbnQ7J+AvEUzM4pYt0Vm5FhinM9CZ26QJm0yBe2seSnqftlYi8PKI7ht27khVMM3rkdz9M5BVor+/D131OV54Ca4ahTIeybXDWDJBWh0rbYkc0RBiUyCb38o9/4eevffyuwUD0/w5QStFYW0HXDZprq1wIBMc+/SfI2eNkR3fy5W0KFdZJew0QTbZtu51nyx8ilB1Gqsskax66jHln8gIX9QnuMVexo4BTqsg+fZFhasxa04x0ljjdOUA9sDFyJbYtXeSu559ECY16ZQy3uYEbXpmOVsuOo2SE6m4grAyMHCTSNdpRnYulPF+55wHWSyX2rSxgeWt85cj9LBdHyfVafOTkp9ixscBf7P1+nt59O47vE1gW97z0PPefeZJUw2dso4pvm9QmpzjU3oO2fpouJunOIqX6GaSdRx+9Dc2vow0fwtn1bsKgh2naCE0niXyizfPoKkF214nXXiIa3Y/oNFGb5yBoogctRG4K5+CHXj7aaNl+1qlo/jGitRdRrRVQCdICLQRlCUSoXiFWzW2jtNUeBDGV1vMYvZhq+TaMqIfrraOpiMzBD+OM30FSPQumg+YU8IIap2yfsfkLOCRcmrqVJ4s91pxVvMwcXXGafecipjag4BXJyjzIUZAak9UZcpUD6OO3Yw4fZNkM+eK2NH8yNkscPMKulSXetlag3LXASvOFOw5x55NzXJjYDhmdH515nOnVCHt5gYgavYJLLMEyYsK3eQg3xj6noTXBnNMwqwLfMZmbnCAuK6p2ntXsCJV2E0N3GF6p4esat5w+iZEk9CyTMxNjhJZFrl1nJZ/GTiRZPyTXC1Cin+9BCkGiC1JBwsWhPB3XAqVIRZKMUWDH6LsI4zbHa19HCJ2CNYI0MpSdPeR6DkYS4esxVe8UneACUkUIkWeyWSfTaSFFghICTSrKHQ/9Ki1qpzMcP/wONFdQ0kMuWgdYlQmGqjJVqlKjQEj/6dJo1bGaEq27QZJKIQs7wSxgBllQCjsooCmjHyoTACZCXOme3NfAGCFMQKGjSF7RNnL1GdX/3h8x3N+GIMZ2a2RSXfKOj9naRjbJUzZD/Nwi63s+RVKeefkedk2kgkutAk71Z/nxn/pHb0yErmIg+teJOAx57gt/wdknH6O6MIdMrtTmDNumMrmd4ug4O2+/i5Fb385nH55hbmaJr60LFrT+ReBIEFp/ioJw60QxVMyQrGE7IUmxyG3rayzmyrywfzcps8UHznwVZ6XJ2y612La4iKEkre376OZrXOy26SUWrp5FMySR1UPsGOUnkr/CltDRtvGV8j7+rx0fZTm91V6gFFoS80//7JN0Mnn+8Ps/8pr2Hl47xX2rj/PEyNs4VTlAIjSkrnOb/zyHqs/zzs+e4kBjAmvH/XR6q9jVC4Trp2jZFQIrTaLrGCpmeO0EAJ5bopOaoFHYjRutoiyfNWecjWIZYWSZXmvTSeVJUjYbdok4OsPw5iwFkVBsBgRuGhKNWGZRymDH3BfBUAg9IikrwryOuGSzUhhmM1/BCgM6rsMLew/x6JE7mIhX2JQlwoJO28wR4DBZjZkbsti+HnH4UogVQ2BKliqKju0wP2T97ZyqSUy5t8kffPLzDFWOopd3EyQ+3vqLOIvHUbEHCJLaLNhZ7B3vRC/vQctPIPQr7Q4y9kjWThGvvghxD+GU0LIjyCRCuWk0O41yBIlYQW/biG6MbCwQrzyPkgFCCaIRhVDQnrL4+odux48LjBXW6QU7eCrYR359g33184x1uuxt+aQ8A00dJGo1aVfPYoVdjMhneds+Tm+/l9X0Ng4KE5CMEtDy5ml0Z/G8NjLZ7M+DIVIIYaJkE9DRrH04eoEwnCVRHoZWYMQsIIs9qvUyaQmCYWR8EfxTtLQEqV9bJZXQSHIlplN19mVmORbvZN4cZcbcTix0XFFgW7OE0kwKzVUMGTGiWoyl6niJQOjLnI7amM1xMCaRmkuWGcbsMxzOzFO0Ixa9Keb8I7TlMLa6xJ7MDxGJHJuxIpQwqgeYmknWMNCFwIs7bLCJYRQ45j3PQjxP3nYpFG7Fs0JC5yy51DqmiAi6GUaaJQ5qLokqsJBpkupMUfT20nhPzP3vfe+blZ6B6P99IIkjls6cJvR6OJkMM088Sm15kdrSAp3aJiM797Dvnvuw0xl23XE31U1Fu9aB3jKt9fOsnJ+huVElUBqdRg2t17y87XQ+T65QxI9i6suLl5d7tovUdCLDpFPMUWjUifMpOpUCbm8T3YuwNwJczyM2TMYzESryaXgmRatHY2yEjp1hqLpCZLksTU3TzmQ5MXyIU7k9l/djJ0F/3IBSIARZ1eId8lHyoo4nXL6u3ktby5FOuuxtzXFb8ywvFvdS9fLUs3mkaSJVf9BQvieZWlmk6CkOyGWm9JP07ITPlx7kS7un2cxdqZVlewm3zwasVBTnRvsNfFaSEBgGlY5HoeezmXXoWQbluMGQvoSSimyrh2jonK7sZbNQYn/tDIYRYMeKKbHISOECF9jFU7yDW9rH2TX/ItnxHs/m7uVFdSvFjRXWh7cTXdXQbYYS209Ib3ZIGl3amo2MBcJL+i+pyAcd7l95jg92m+wdugOjvAtdv7oxeetcUYqaV6fh1TibtQhEk/MHjrDfE7xnNSZ9pe5AqBJ0NAINPE2QSRQ2gkgphAADgVSKhgENIVm3JAu6QUPBdLJC1lhECo0okVjpGpYREBKjp6vkxk5iKJPU5kHKcx9E7xWJnVWUL/BGTxGnPCJnk8RqYczdx/LyIeZii9gQuGlI9A2szRfxu/O0TA3PzuLYZYyxo3yPV2bK26pZqwShGSiZINurqLBNUr9IvPICKuyiKnvwRvegRT613kU8rYuWSlMs+hw3czhxmo7/PaClkdoFusZZYhnhxi6GzKExhab1u/wKGSOUJNNdYvfsp6mE54k9nY1CAU0maAqMOCHr9dvAhCHRi5KX9u/nfG4780Pj/INzX2E436OcHaIoA7pamk3ejU4TJ5mn3Z1nvtugFrrUYpeS6eELnXo3DULDyRWxIg9d+jQCeTljlwKk5aCFAQiBli7x/l/45xy85TbeLAPR/3uMkpKXvv4Qz33hL9hcvASAm82RHxmlOj9HHIUgBJXJ7eSGhkmiCDuVZvLQrQxN7WB9/gJLZ06xNHMK3TA4eP+7Gd61hyfcAnU3y8bGFxjpPcw9WYlSCb6/RBCsAAJNM4nDiNrZPN2VFM35DLopyW3vELZNgqaFkgLdSghaFirpP+YKSxHYaRqpAm0nS9dNY4YhlgpZ2DaNn3YY9Tc4unEKfb2N39bR/ICd+SZ2Qeep/BEuDU1Sy2WZze5EomFHCU23SGAa/UY+AKVwgx6RbhKbFgW/zfsWH+Ed1cc5WZ7mS0PvYaEwTSpsc0v7OO/Tv8hUfoGvJu/jrL6fjsqSS5rYUYt5hohVCUeP6WgppCYZSVa4v/Y42+ITOJ2EaDFFez4DCjRb4iQR2nhMHBqIWFKZapPa2SUJ0ggVU1c5Vlu7CRtZXOUhcaisNWnpGb7q3MaKylHRmkyLNZTSiTWHYa2LIRRKaoS9HVSUTTZOk0tcSrpOomA5kvivuhR9U3Bq0qKdERQRoAuODxnMFbZuglfFC15OvymU4mg94W2bCXvbCXvbktGtDTcNeKmgs6stWUhrrJlwqCWpBApTKhwENSV5Mp3w1fGYiyMGShc84J3klF3hrDWNkgb5rsKSkoKmsa2d0HYEphKEmuCZko5v9Mt112bA96wn5CLBhi3wdMFSrs5irkqXIr5wSMmIXCLpGCaO6DKaVJkIe0x2IS/m2dkBV1kYYYbU5mGUHhKklxCJTS+KWd4ssdqpEGgvB/AVhgyxemukm6cw4hYyP8xcfgKhT+Mog0DroksPQ7qADkToqkfWXCOjrzCUPQ7zOnI9hVXbJN1bI0lr6HGC5ktSUyH5qS5JJkWVXbhxgBZZhLKA7vqMps/gJZNknGVaUYunqpNc7JbImx62LilZAQWrgwIaUZqGb5GOYjasEqHl8P5f+jgT0zvftK4MRP+7AKUUXrtFa32NJz/zp8RhQHnbFFOHb2Vi/yGcdOYt21cYVhHCQtdTdHvn6bRPE0U1NJElmz9Myplg8dwTrM31ePRCh4uBjmecYI86i+Mr0vUm3SUHGb+qy5lQvLIVDTShSPVCQNBzLKR4ue/5azORarKkl7lQ3MnC2A7q+TJWFHB45nkmly8iAKVrGA5kjQiZySFb4PU8EgFhIUVXJBQ2PF4dEGinsjx8zweY2X3LZZG04pis38IzbIhOk23N44QBqA6F+ixS26SeSfAcAzcImahOk+5N0MwWaeRMhLyIFMtsFgsoLYPdPUXZt8mHWYp+nvFgGymlyIkGjrbKWbfHip6mYdUpSUUmMdDsCD/bIvSLjK3eQazFFJVLRqYphUVSwTC2NDnnzBEID6kEYeKwqUN1JI/v2Ex0eow361zKpNjIlKhJi/WmQ6CZmAbs7nRZtwTEFttDkx+SNtvROJPWGPMl22PBvCM4W9BRmqBhCu7ejDnclPgaBBrktzr5eBrM2wKUoiChFIH1Gi6NhOS8HZCIhMNehpCEphaTkyb2Vpx804TZFGRD6OmCY0VoWwF7e4LtPRNNaZzN6sxmNUbDLppVRVlNdkZrjKafJEkvoUSM5Q1j+EXM9jiiegs6inblFEbioHdHCYICzd4QvkgoJC6uNPASiBNFWggSAU0p6cqEnoJmDDmlsc8x2GYJpILTvmQxTBBCYdCvoSfoxIi/dUZrQMUQlHTFRqzoJBJLdiiqFTTVJHDOkK9ewvIDZElgjcUoJ49jtTnsnyUROi9at3Lo5/6CzLdw7Q9Ef8C3zdm1Nv/1yXmena8zs1pnV+48ruETxSYEgAaT5SVG6uuU9DrpVJdcpkNpqkkjLHCpcwCBRdbySSdF9PVlgqhLJHV0emSUR7CeobqQQhg6TqSwZIZetsQu+xgylohEMmx1KZo+XT3LkNVk2KoBEAidRAhMJKaUtCMLPzE4ldrOjLGNKDHoThRpulkyqkdOhgwlHQ4Gi5jSRgTbafkHOJdZZ80WeJrLHm+GOTvNBXmSfFTl+zoh93r1VxyXmsryNXWEz6cfYD3Js9zJErhLJEaXJBjjtkCnrDRc0WRO5VgTNmVtk7zSsFXCEjk8pZMRHVJGFeEuYbqXaDgtFDq5uMLR3g52hru4s7cPhaSt1amKFg3hM6xBpAu6WptLpuS8NsJ4IpAqYd7pEbHJkXYGO7axMdgUbdqEeJhsyhQrSY42NrqI8RKLxDawijqOEeErg4M1i1s9C1vp1CWEQjGKznahkQjJpojoSclp4TOPQYSJB+QR3IvBnRiklOAxEfAZrYsjBLrUmVUa78bgQSzKCDQULhrlrZtBF8UMCULAHjQySkPy6uFmbwzPiHBjE7nVefXVdMwYO9Ew5ZWtKxQC0a+MSTA1MEX/e6T61ZZk610TEMp+OM0HGpZGV4MgkHgKslKhW4K2EKwpxZqrkZcwnEDHho4AvZXgdCRWApZQaELgGgkf+XfvvTwu5s0wEP0BbyltP+L4QpNaL6SSsTg8kaftx9Q6IbVeSCllkbZ1zq3MUd/8DEQXyGvHUErixQ6u0WahPUE7zJG3OyhsgsRlIn2OvN2+vJ9EGmiiX7N6+bufpEmUhqV5OLpHoRWTb0YYIcSxhZe4bBg57EKLStSi2IjRQ+jpFlYocaOYrrApxB6u+ttdE19GKXF5v5Eco5N8P6E8gClmsbUXSMgTqWk0ehhijZ44TCgMzmWzZOMMRnuIL0iDLxDio0hQjKAxsTVpQyR8Is2nYrRIGV260sRLbBpYLIRFkqsmvHsr6AtrH5OYUQTbEbREj46yOSA8IGRTBHS0kEQkjGgdUiLGQZBSLoZMs6lMXHQmVZo8CluLKcZZNOViYdEhoYtHmnWqYp1h7Ry5pMeactmIR4mTCrHKs55UsOM0OV1jyA5J2z69yMRTglZksC4Ea4ZiQZecFwmhgDaKIQQpBM2SxVTZZVLTEUKwZgmWDUUExH6MsnWmfMVGWuNsud/TaCTssq/ZYdE1aNoaaRURaDabRpoEg91tybgvGfUUe9oRTdfjb0ZD1m0DKQ0OtQTv2IgZ8xRKgh3pCGXQ0zT29CCdgCtfxwmvQyigagvGfYWvQc0ULFjwg//rvQPRH/DdiVJbI2KFYLnh8dx8nbfvLDGcdbZ+V5xfb3Hs/BPIpE61MUMUNdA1E9e26QaSMGrjGl1cE3Q9h2Vmscw8m+E+LrYm8CKBY2gYuqDejah2fMoZi0rGoelF3D5VZOdQmomCS63RYX3lEgrJuNmhs7lEZ3WBnhR4mUkypRHssEbKyOCmymSzDsW1GTIXnsQ2Agw2Eak0FIaJEkFntYeshf050A2BTBS9xGKRPJuqQtoZZZTTpIIFRJwi0SIs0cERDSxquGqdrKoCECkdT1lINFLCR0MRo3Nc7WJRDrOpKvhkcBRUKVEUCyTKxVf7KKgs6yLBxCNNBqE0NkXCKiYIr9/WrhzOkGFV6YzQReJwUfRHZlsoxtBJI5gjofdN/GorMFB0t4TJQDJETJ6IHhrrWPivuIEpbCICLAwFOdnv99/U/lZk8JpUgDIa8yQkIiSth1hJRKQMOrikCIkRRJjEGCSGhrJ1RPflQMzLO+pPgawQGEaEcnRwdfQ0hLaLcg2EJnG0gLTRBQ18I4VnppCajkWIq3rYcYCjfHQZkwtbDPk10hGEMo8mdTzNgVCS6TmMhAalqMcCBi2rx5ifJicdXM2mgMWSK9EMl6FQJ6DDR//lB9/YQXkVb6noCyHeD/w7+q0ev6+U+vVX/W4D/xm4A9gE/qFSam7rt48BP0l/BtT/WSn1pdfb10D0B9xU+C2oXYBUGbJjoBvEgUd16QKGismPbifWbDyvP/d+u92m1WpdfjdNk507dzI5OYlhGPi+jxAC27ZfsZuXr/NWq8XZ0zOsr68TRA6RiBgyWhRRyCBLqpfjQk+xSULdkkQiYaero9lpakKj6kk2/IQekpEUWIbOyuIyDS8gimMyssOw3GBYrjApVjEQ1GQZVEyiEqqyyKwaJ8SiKH0QId0kje6biNgg0BykZlAOO5iqi2cKMqLNHhaZEHXWjDx+kqKkdakYbSxNIvQIkza6CEg0gSkimtjMqCnapFimglIGrooJhElTZMkpj1WZRlchCRobokAsNTQUPjZVkaMnHCTi8hTfbxZNJNh6gFQaYWJRdmtE0sTRA0wtIkhswsREKo321nQaE+llHvvff+pb2t8bFf1rzyVwZUM68AngfcAi8IwQ4nNKqVNXrfaTQF0ptVsI8RHgN4B/KIQ4CHwEOASMAw8JIfYqddVQxAEDbmacHIwfecUiw3YZ3Xno8ncTcN1+V9FSqfT6m3Oc11z+crggn89z191ve91tHPhmZf4OopQiSAJiGZM2+1NOdKMujVaNdq1BJmrRilo0oxYzUYtm0GTFX+FE4yRtqbAjkw4dPNEFTmNKA0PpCMTWxBT96ToUsD0Yw1A6nhYgEIyFJXYE4wzFRSRLtPQOkRZTiPL4aKxLmyiy0DQFeo9CqEhLC0O6REonRCdIbOrKJkVMSqVIh2lMqdEWCUmQpqtMNMNA10JMzaforFGWGvmcR6IlyORvd+d9q/mmog+8DTivlLoAIIT4E+BDwNWi/yHgV7Y+fwr4D6J/ln0I+BOlVABcFEKc39reE29N8QcMGHAjIYTAMV5548pYGTKVDFSm3vB2EpkQyYhQhkRJRCQjoiQiSAK82KMX9+hFPUzdRBMasYyJZYylW1iahZ/4NIIGDb9BK2yRUpLtKKSSJFISSZ1QhjSTFmFSxdRMMlaGipFi6HI8vt8BQEgYDg36zUWi/662pgJUKWpGSKiPUNDzjGXG3pLj+Hq8EdGfABau+r4IvP1a6yilYiFEEyhvLX/yVf+dePUOhBA/Dfw0wNTUG3fsgAEDBrwWuqajazoOr/3kczPzRoJVr9XU8uqGgGut80b+i1Lq95RSdyql7hwaGnoDRRowYMCAAd8Kb0T0F4Gr0xttA5avtY4QwgDyQO0N/nfAgAEDBvwd8UZE/xlgjxBiWghh0W+Y/dyr1vkc8NGtzz8MfE31uwt8DviIEMIWQkwDe4Cn35qiDxgwYMCAN8s3jelvxeh/FvgS/S6bn1RKnRRC/CrwrFLqc8AfAH+01VBbo39jYGu9P6Xf6BsD/2zQc2fAgAEDrh+DwVkDBgwYcAPwRvvpf2ujDgYMGDBgwHclA9EfMGDAgJuIgegPGDBgwE3E37uYvhBiA5j/NjZRAapvUXG+GxjYe+Nzs9l8s9kLb43N25VS33Sg09870f92EUI8+0YaM24UBvbe+NxsNt9s9sLfrc2D8M6AAQMG3EQMRH/AgAEDbiJuRNH/vetdgL9jBvbe+NxsNt9s9sLfoc03XEx/wIABAwZcmxuxpj9gwIABA67BDSP6Qoj3CyFmhBDnhRC/fL3L851CCDEnhDghhHhBCPHs1rKSEOIrQohzW+/F613ObxUhxCeFEOtCiJeuWvaa9ok+v73l8xeFELdfv5J/a1zD3l8RQixt+fgFIcSDV/32sS17Z4QQ/931KfW3hxBiUgjxsBDitBDipBDi57eW35B+fh17r4+flVLf9S/6E8HNAjsBCzgOHLze5foO2ToHVF617N8Cv7z1+ZeB37je5fw27HsAuB146ZvZBzwIfJF+3oa7gaeud/nfInt/BfjF11j34Na5bQPTW+e8fr1t+BZsHgNu3/qcBc5u2XZD+vl17L0ufr5RavqXUzoqpULg5ZSONwsfAv5w6/MfAh++jmX5tlBKPUJ/ptaruZZ9HwL+s+rzJFAQQnzn8829hVzD3mtxOf2oUuoi8HL60e8qlFIrSqljW5/bwGn6GfVuSD+/jr3X4jvq5xtF9F8rpePrHdTvZhTwZSHEc1tpJgFGlFIr0D/BgOHrVrrvDNey70b2+89uhTI+eVW47oazVwixAzgKPMVN4OdX2QvXwc83iui/obSMNwj3KqVuBz4A/DMhxAPXu0DXkRvV778D7AKOACvAb20tv6HLHEDcAAABh0lEQVTsFUJkgE8Dv6CUar3eqq+x7LvO7tew97r4+UYR/ZsmLaNSannrfR34DP3HvrWXH3e33tevXwm/I1zLvhvS70qpNaVUopSSwP/HlUf7G8ZeIYRJXwD/q1Lqz7cW37B+fi17r5efbxTRfyMpHb/rEUKkhRDZlz8D3wu8xCvTVX4U+Oz1KeF3jGvZ9zngf9jq3XE30Hw5PPDdzKvi1f+Avo/hBkk/KoQQ9LPtnVZKffyqn25IP1/L3uvm5+vdsv0WtpA/SL9VfBb4V9e7PN8hG3fSb9U/Dpx82U6gDHwVOLf1XrreZf02bPxj+o+6Ef0az09eyz76j8Gf2PL5CeDO613+t8jeP9qy58UtARi7av1/tWXvDPCB613+b9Hm++iHK14EXth6PXij+vl17L0ufh6MyB0wYMCAm4gbJbwzYMCAAQPeAAPRHzBgwICbiIHoDxgwYMBNxED0BwwYMOAmYiD6AwYMGHATMRD9AQMGDLiJGIj+gAEDBtxEDER/wIABA24i/n+HQi4Jbg5sQAAAAABJRU5ErkJggg==\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 24,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Random variables and probability distributions"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "https://www.investopedia.com/articles/06/probabilitydistribution.asp"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Cumulative Distribution "
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "data = df['Adj Close']\n",
        "values, base = np.histogram(data, bins=40)\n",
        "#evaluate the cumulative\n",
        "cumulative = np.cumsum(values)\n",
        "# plot the cumulative function\n",
        "plt.plot(base[:-1], cumulative, c='blue')\n",
        "#plot the survival function\n",
        "plt.plot(base[:-1], len(data)-cumulative, c='green')\n",
        "\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 25,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sorted_data = np.sort(data)  # Or data.sort(), if data can be modified\n",
        "\n",
        "# Cumulative counts:\n",
        "plt.step(sorted_data, np.arange(sorted_data.size))  # From 0 to the number of data points-1\n",
        "plt.step(sorted_data[::-1], np.arange(sorted_data.size))  # From the number of data points-1 to 0\n",
        "\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 26,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Probability Density Function"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Probability Density Function (PDF) is continuous random variable and have value that is given sample in the sample space can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample. (Wikipedia)"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "values = df['Returns'][1:]\n",
        "x = np.linspace(values.min(), values.max(), len(values))\n",
        "loc, scale = stats.norm.fit(values)\n",
        "param_density = stats.norm.pdf(x, loc=loc, scale=scale)\n",
        "label = 'mean=%.4f, std=%.4f' % (loc, scale)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(10, 6))\n",
        "ax.hist(values, bins=30, normed=True)\n",
        "ax.plot(x, param_density, 'r-', label=label)\n",
        "ax.legend(loc='best')\n",
        "ax.set_title(\"Probability Density Function\")"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 27,
          "data": {
            "text/plain": [
              "Text(0.5,1,'Probability Density Function')"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 27,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Log return goes up and down during the period\n",
        "df['Returns'].plot(figsize=(20, 8))\n",
        "plt.title(\"Stock Daily Returns\")\n",
        "plt.axhline(0, color='red')\n",
        "plt.ylabel('Daily Returns')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 1440x576 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 28,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sns.distplot(df['Returns'].dropna(),bins=100,color='red')"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 29,
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x20b92d1c6d8>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 29,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Cumulative Probability Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "values = df['Returns'][1:]\n",
        "x = np.linspace(values.min(), values.max(), len(values))\n",
        "loc, scale = stats.norm.fit(values)\n",
        "param_density = stats.norm.cdf(x, loc=loc, scale=scale)\n",
        "label = 'mean=%.4f, std=%.4f' % (loc, scale)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(10, 6))\n",
        "#ax.hist(values, bins=30, normed=True)\n",
        "ax.plot(x, param_density, 'r-', label=label)\n",
        "ax.legend(loc='best')\n",
        "ax.set_title(\"Cumulative Probability Distribution\")"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 30,
          "data": {
            "text/plain": [
              "Text(0.5,1,'Cumulative Probability Distribution')"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 30,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Binomial Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import binom\n",
        "\n",
        "n = len(df['Returns'])\n",
        "p = df['Returns'].mean()\n",
        "k = np.arange(0,21)\n",
        "binomial = binom.pmf(k,n,p)\n",
        "\n",
        "plt.plot(k, binomial, 'o-')\n",
        "plt.title(\"Binomial: n=%i, p=%.2f\" % (n,p), fontsize=15)\n",
        "plt.xlabel(\"Number of successes\", fontsize=15)\n",
        "plt.ylabel(\"Probability of successes\", fontsize=15)\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 31,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "s = np.random.uniform(values.min(), values.max(), len(values))\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "count, bins, ignored = plt.hist(s, 15, density=True)\n",
        "plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 32,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "binom_sim = binom.rvs(n = n, p = p, size=10000)\n",
        "print(\"Mean: %f\" % np.mean(binom_sim))\n",
        "print(\"SD: %f\" % np.std(binom_sim, ddof=1))\n",
        "plt.hist(binom_sim, bins = 10, normed = True)\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"Density\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean: 2.484000\n",
            "SD: 1.556980\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 33,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Poisson Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "rate = 3 # Error Rate\n",
        "n = np.arange(0,10) # Number of Trials\n",
        "y = stats.poisson.pmf(n, rate)\n",
        "y"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 34,
          "data": {
            "text/plain": [
              "array([ 0.04978707,  0.14936121,  0.22404181,  0.22404181,  0.16803136,\n",
              "        0.10081881,  0.05040941,  0.02160403,  0.00810151,  0.0027005 ])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 34,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(n, y, 'o-')\n",
        "plt.title('Poisson: $\\lambda$ =%i' % rate)\n",
        "plt.ylabel('Probability Error')\n",
        "plt.xlabel('Number of Errors (out of 100 trials)')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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eW42quh3HmCZnxSKEbd9Xwb+/3cLlQ9Lp0a6523GiWsukeO64oA/fbNrNR3Znt4lCVixC2LPzc6mtVW4ZZUcVoeDqU7vSu0MKD76/hsrqWrfjGNOkrFiEqOK95bz2XT6TsrpwUttmbscxQFxsDHeNO5m8XQd55ZstbscxpklZsQhRz8zPRVFuGtnb7SjGy3l92nNuRjue/GQDpQcr3Y5jTJNpsFiISKyIzGuqMMajYM9B3liUz5VZXenS2o4qQomIcPe4fpRVVPH4vA1uxzGmyTRYLFS1BjgoInatYBN6Zn4ugthRRYjK7NSCyaedxL+/2cLGkv1uxzGmSQRyGqoCWCEi/xSRJ+sewQ4WrfJ3H2RGdgFXn9bVupYIYXeM7kNSfCwPvr/W7SjGNIlAisV7wD3A58Bir4dfIjJWRNaJSK6I3Olj/nARWSIi1SIysd68GhFZ6jxmB/J+keCpTzcQEyP8yo4qQlr7Fon8amQv5q3Zzte5O92OY0zQ+b2DW1VfFpEEoG4Mz3Wq6neAYhGJBZ4BLgAKgEUiMltVvcer3ApcD/zWxybKVXWwv/eJBLNyCg/rVmJ4Rjs6tkxyO5bx47/P7sGr32zl/vfWMOeWc4iNEbcjGRM0fo8sROQ8YAOeD/5ngfUiMjyAbZ8G5KrqJlWtBF4HxnsvoKp5qrociNqL1mflFDJ15goKnUIB8N3m3TbIThhIio/lzov6sqZ4H28tLnA7jjFBFchpqEeBC1V1hKoOB8YAjwWwXjrgPYJMgTMtUEkiki0i34jIBF8LiMiNzjLZJSUlx7Dp0DFt7jrKq2oOm1ZRXWuD7ISJSwZ2ZshJqUz7aB0HDlW7HceYoAmkWMSr6vefXKq6HogPYD1fx+TH0qnOSaqaBfwYeFxEeh2xMdXnVDVLVbPat29/DJsOHTbITngTEe65pB8lZYf4x2cb3Y5jTNAEUiyynSuhznMe/0dgDdwFQFev112AokCDqWqR83UTsAAYEui64cQG2Ql/Q09qzaWD0njui01W5E3ECqRY/BJYBdwK3AasBn4RwHqLgAwR6eE0kE8GArqqSURai0ii87wdcLbzvhFnyphMEmIP/zEkx8faIDth5vdjM6lV7PShiVh+7+AG/qmqf1XVy1X1R6r6mKoe8rdhVa0GbgbmAmuA6aq6SkTuE5HLnO2fKiIFwCTgHyKyyln9ZDxHNMuA+cBD9a6iihgThqTTt1MKMeI5b5eemsyDl59ig+yEmS6tm/Gzc3rwdk4hy/JL3Y5jTKMTf33zi8hc4FLniqaQlZWVpdnZ2W7HOGa7D1Ry+l/mcd2Z3bn7kn5uxzEnoKyiipGPLKBHu+ZM//mZiNiltCb0ichip324QYGchsoDvhKRe0Tk13WPE05oAM+ls1U1yqSsrv4XNiGtRVI8v74gk0V5e/hw5Ta34xjTqAIpFkXAHGfZFl4Pc4JUlenZ+Qzs0orMTrZLI8FVp3alb6cWPPjBWg5V1/hfwZgw0eAd3E6bRYqqTmmiPFFlVdE+1m4r4/4JA9yOYhpJbIxw17iT+ck/v+Plr/O4cfgRV3wbE5YC6XV2aBNliTozsvNJiIvhsoFpbkcxjejcjPaMzGzPU5/ksmu/32tBjAkLgZyGWiois0XkJyJyed0j6MkiXEVVDbOWFjGmfydaNQvkHkcTTu4adzIHq2p44hMb88JEhkCKRRtgFzAKuNR5XBLMUNFg3prt7C2v4sqsLm5HMUHQu0MLrjn9JF79disbtpe5HceYExZIr7M3NEWQaDMju4C0Vkmc1aud21FMkNx2fgZv5xTyl/fX8OINp7kdx5gTctQjCxGZ7vX84XrzPgpmqEhXvLeczzeUMHFYF+vWOoK1TUnkllG9mb+uhM/Xh2dHl8bUaeg0VIbX8wvqzQvPXvtCxMwlhajCxGF2b0Wku+6s7pzUphl/fm8NNbXH0o+mMaGloWLR0G+2/dYfJ1VlRnY+p/dow0ltm7kdxwRZYlwsUy/qy7rtZUzPzve/gjEhqqFi0UxEhojIMCDZeT607nUT5Ys4i/L2kLfrIFfaHdtRY+yATpzavTWPfrSOsgq/g0waE5IaKhbFwF+BR4BtzvNHvV6b4zAjO5+UxDguOqWT21FMExER7h7Xj537K/nbAhvzwoSno14NpaojmzJINDhwqJr3VhRz6cA0miX4vRDNRJBBXVP50ZB0nv9yMz8+/SS6tLZTkCa8BHKfhWkk760o5mBlDVeeavdWRKMpYzKJEfjfD23MCxN+rFg0oTezC+jZvjlDT2rtdhTjgrTUZG48tyezlxWxZOset+MYc0ysWDSRzTsP8F3ebiYO62LjHESxn4/oRfsWidw/ZzX+xpIxJpT4LRYi8paIjBMRKywn4M3F+cQIXDHUTkFFs+aJcUy5MJOcraXMWV7sdhxjAhZIAfgb8GNgg4g8JCJ9g5wp4tTUKm8tLmREn/Z0bJnkdhzjsiuGdaFf55Y89MFaKqpszAsTHvwWC1Wdp6rX4OmqPA/4WES+FpEbRMS6Sw3AFxtK2LavwkbDM4BnzIu7x51MYWk5L3y12e04xgQkoFNLItIWuB74GZADPIGneHwctGQRZMbiAlo3i+f8kzu4HcWEiLN6t2P0yR15dv5GSspszAsT+gJps5gJfAE0Ay5V1ctU9Q1VvQVICXbAcFd6sJKPV21n/OB0EuNi3Y5jQsjUi/tSUVXDY/PWux3FGL8CObJ4XlX7qeqDqloMICKJAKqaFdR0EeCdpUVU1tRa9x7mCL3ap3DtGd14/butrNtmY16Y0BZIsXjAx7SFjR0kUs1YnE//tJb0S2vpdhQTgm4fnUGLpHj+/P4at6MY06CGxrPo5KMTwaEich6eU1LGj9VF+1hZuI9Jw+xyWeNbarMEbj0/g8/XlzB/3Q634xhzVA11UDQGT6N2FzydCNYpA/4QxEwRY8bifBJiYxg/ON3tKCaE/eSMbryyMI8/v7eGc3u3Iy7Wbmkyoeeov5Wq+rLTmeD1qjrS63GZqs5swoxhqbK6llk5hVzQryOtmye4HceEsIS4GKZefDK5O/bz2iIb88KEpqMeWYjItar6b6C7iPy6/nxV/auP1YzjkzXb2XOwiolZdgrK+Hdhv46c3qMNj328nvGD02iZZLcwmdDS0PFuc+drCtDCx8M0YMbiAjq1TGJ4ho1Aa/wTEe65pB97DlbyzKe5bscx5ggNjWfxD+fr/zRdnMiwfV8FC9bt4BcjehEbY50GmsAMSG/FFUO78OJXeVxzejcbdteElIZOQz3Z0Iqqemvjx4kMM5cUUqsw0a6CMsfotxdm8t7yYh7+cC3PXDPU7TjGfK+hq6EWN1mKCKKqzFicz6ndW9Ozvd3gbo5Np1ZJ/HxETx6ft4Eb8naT1b2N25GMARo+DfVyUwaJFEu2lrKp5AC/GN7L7SgmTN04vCevf5fP/XNW8/avzibGTmWaENDQTXmPO1/fFZHZ9R9NFzG8zMjOJzk+losHdnY7iglTzRLimDImk2UFe5m9rMjtOMYADZ+GesX5+khTBIkEByurmbO8mHEDO5OS2NCuNaZhPxqSzotfb+bhD9cypn8nkhOsE0rjroZuylvsfP0MT19Qe4DdwEJnmqnnw5Xb2H+o2rr3MCcsJka4Z1w/ivdW8M8vN7kdx5gGjywAEJFxwN+BjYAAPUTk56r6QbDDhZvp2fl0a9uM03pYo6Q5caf3bMvY/p144pMN/PubrWzfV0FaajJTxmQyYYh1IWOaViCd0DwKjFTV81R1BDASeCyQjYvIWBFZJyK5InKnj/nDRWSJiFSLyMR6864TkQ3O47pA3s9NW3cd5JtNu5k0rAsi1iBpGsewbq2pqlG27atAgcLScqbOXMGsnEK3o5koE0ix2KGq3reUbgL8do8pIrHAM8BFQD/gahHpV2+xrXg6K/xPvXXbAPcCpwOnAfeKSOsAsrrmzSUFiMDlQ+0UlGk8L32dd8S08qoaps1d1/RhTFRr6Ka8y52nq0TkfWA6oMAkYFEA2z4NyFXVTc72XgfGA6vrFlDVPGdebb11xwAfq+puZ/7HwFjgtQDet8nV1ipvLS7g3Iz2pKUmux3HRJCi0vJjmm5MsDR0ZHGp80gCtgMjgPOAEiCQ//LTAe8uNAucaYEIaF0RuVFEskUku6SkJMBNN76vN+6isLTcGrZNozvaPx/2T4lpag3dlHfDCW7b14l7bcx1VfU54DmArKysQLfd6KZn59MyKY4L+nV0K4KJUFPGZDJ15grKq2q+nxYfK0wZk+liKhONArkaKgn4KdAfz1EGAKr6335WLQC8B57uAgR6h1EBnqMY73UXBLhuk9pbXsXcVdu46tSuJMXbtfCmcdVd9TRt7jqKSsuJj41BUQakt3I5mYk2gTRwvwJ0wtOO8BmeD+5ARpdfBGSISA8RSQAmA4He+T0XuFBEWjsN2xc600LOu8uKOFRdy6RhXf0vbMxxmDAkna/uHMXmh8bx+e9G0iIpnpteXUJ5ZY3/lY1pJIEUi96qeg9wwOkvahxwir+VVLUauBnPh/waYLqqrhKR+0TkMgAROVVECvA0mv9DRFY56+4G7sdTcBYB99U1doeaGdn59O3UggHpLd2OYqJAp1ZJPHbVYNbvKONPs1e5HcdEkUD6pKhyvpaKyABgG9A9kI2r6vvA+/Wm/dHr+SI8Ryq+1n0BeCGQ93HL+u1lLCvYyz2X9LN7K0yTGdGnPTed15un5+dyes82drm2aRKBHFk855wKugfPaaTVwMNBTRUmZmTnExcjTBic5nYUE2VuH53BaT3acNfbK8ndEchZYWNOjN9ioarPq+oeVf1MVXuqaoe6UfSiWVVNLW/nFHL+yR1om5LodhwTZeJiY3jq6iE0S4jlpldzrP3CBJ3fYiEibUXkKadbjsUi8riItG2KcKFs/tod7NxfyZVZ1rBt3NGx5Q/tF/fOXul2HBPhAjkN9Tqe7j2uACYCO4E3ghkqHMxYXED7FomM6NPe7Sgmig3v056bR/ZmenYBby0ucDuOiWCBFIs2qnq/qm52Hg8AqcEOFspKyg7x6dodXD4knbjYQHahMcFz2/kZnN6jDXfPWsmG7dZ+YYIjkE+6+SIyWURinMeVwHvBDhbKZuUUUlOrTMqyq1CM++raL5onxvKrV5dwsLLa7UgmAjU0rGqZiOwDfo6nV9hK5/E6cEfTxAs9qsr07HyGnJRK7w4t3I5jDAAdnPaL3JL93PuO3X9hGl9DI+W1UNWWztcYVY1zHjGqGrV3oC0r2MuGHfvtjm0Tcs7NaM8tI3szY3EBb1r7hWlkAQ0U7dxxPdx5uUBV5wQvUmibkZ1PUnwMlwzq7HYUY45w2+g+fJe3m7tnrWBgl1b06WhHv6ZxBHLp7EPAbXhuxlsN3OZMizoVVTXMXlbERQM60zIp3u04xhwhNkZ4cvIQUhLjuMnaL0wjCqSB+2LgAlV9wemCY6wzLerMXbWNsopqa9g2Ia1DyyQev2oIuSX7uWeWtV+YxhHodZ/el8pGbd/IM7IL6NI6mTN6RP09iSbEnZPRjltGZfDWkgJmZOf7X8EYPwIpFg8COSLykoi8DCwG/hLcWKGnYM9Bvtq4k4nDuhATY50GmtB32/kZnNmzLfe8s5L1dv+FOUENFgvxdKX6JXAGMNN5nKmqrzdBtpDy1uJCACba0KkmTMTGCE9cPZiUxHi7/8KcsAaLhaoqMEtVi1V1tqq+o6rbmihbyKitVd5cks9ZvdrSpXUzt+MYE7AOLZJ4YvJgNpbs5+5ZK/H8SRtz7AI5DfWNiJwa9CQh7JvNu8jfXW73VpiwdHbvdtx2fgYzlxQyw+6/MMcpkGIxEk/B2Cgiy0VkhYgsD3awUPJmdgEtkuIYO6CT21GMOS63jMrgrF5t+eM7K1m3zdovzLELpFhcBPQERgGXApc4X6NCWUUV768s5tJBaSTFx7odx5jjEhsjPD65rv1iMQcOWfuFOTYN9Q2VJCK3A1Pw3FtRqKpb6h5NltBlc5YXU1FVyyRr2DZhrkOLJJ68ejCbdx6w9gtzzBo6sngZyAJW4Dm6eLRJEoWYGdn5ZHRIYXDXqO6V3USIs3q147bz+/B2TiEzsq39wgSuoWLRT1WvdYZQnQjWwqaPAAAU9ElEQVSc20SZQkbujv0s2VrKpKwueK4iNib83TyqN2f39tx/sXbbPrfjmDDRULGoqnuiqlF5gnPG4nxiY4QJQ9LdjmJMo4mNER6/aggtkz33X1j7hQlEQ8VikIjscx5lwMC65844FxGtuqaWmUsKGZnZgQ4tktyOY0yjat8ikScmDybP2i9MgBoazyLWGc+ibkyLOK/nET+exWfrSygpO2SdBpqIdVavdtw+2tN+8cYi6z/KNMwGkD6KGdkFtEtJYFTfDm5HMSZobhrZm3N6t+Pe2atYUxzxJwzMCbBi4cOu/Yf4ZO12JgxOJz7WdpGJXHX3X7RKjuemV5ew39ovzFHYJ6EPs5YWUVWjTMqy7j1M5GuXksgTk4eQt+sAd729wtovjE9WLOpRVWZk5zOoSysyO9mQlCY6nNmrLXeM7sM7S4t43dovjA9WLOpZVbSPtdvKmGhHFSbK3DSyN+dmeNovVhdZ+4U5nBWLeqZn55MQF8NlA9PcjmJMk4qJER67ajCpyfHc/B9rvzCHs2LhpaKqhneWFjG2fydaNYt3O44xTa5dSiJPXu1pv/jDTGu/MD+wYuFl3prt7C2vsnsrTFQ7o2dbfnNhJrOXFfHad9Z+YTysWHiZnl1AWqskzurVzu0oxrjqlyN6cW5GO/70rrVfGA8rFo7iveV8saGEicO6EBtjnQaa6BYTIzx+1WBaN4vnpv8soayiyv9KJqJZsXDMXFKIKky0oVONAaBtSiJPXT2ULbsOMNXaL6JenNsBQkHdvRWn92jDSW2buR3HmJBxWo82/ObCTKbNXUdyQixf5+6iqLSctNRkpozJtB6Zo0hQjyxEZKyIrBORXBG508f8RBF5w5n/rYh0d6Z3F5FyEVnqPP4erIyzcgo59c/zyNt1kPXby5iVUxistzImLP1yRC8yO7VgRnYBhaXlKFBYWs7UmSvs7yWKBK1YiEgs8AyeUfb6AVeLSL96i/0U2KOqvYHHgIe95m1U1cHO4xfByDgrp5CpM1ewc38lAHsOVtkfgDH1xMQIe8uPbLMor6ph2tx1LiQybgjmkcVpQK6qblLVSuB1YHy9ZcbjGb4V4E3gfGnCIemmzV1HeVXNYdPsD8CYI23fW+FzelFpeRMnMW4JZrFIB7wv0i5wpvlcxhmNby/Q1pnXQ0RyROQzEfE5pKuI3Cgi2SKSXVJScswBj/aLbn8AxhwuLTX5KNNtYLBoEcxi4esIof7lFEdbphg4SVWHAL8G/iMiRwy4pKrPqWqWqma1b9/+mAMe/Q/A93RjotWUMZkkx8ceMb1DiyTrFiRKBLNYFADe16F2AYqOtoyIxAGtgN2qekhVdwGo6mJgI9CnsQP6+gNIjo9lypjMxn4rY8LahCHpPHj5KaSnJiN4jijGndKJZQWlXPb0l6zbVuZ2RBNkwbx0dhGQISI9gEJgMvDjesvMBq4DFgITgU9VVUWkPZ6iUSMiPYEMYFNjB6y77G/a3HV2OaAxfkwYkn7E38bCjbu45bUcxj/zJQ9MOIWJw6yrnEglwbzRRkQuBh4HYoEXVPXPInIfkK2qs0UkCXgFGALsBiar6iYRuQK4D6gGaoB7VfXdht4rKytLs7Ozg/a9GGN821FWwa2v5fDNpt1cldWV/xnfnyQfp6xMaBKRxaqa5Xe5SLkr04qFMe6prqnlsXnreWb+Rk7u3JJnrxlKj3bN3Y5lAhBosbDuPowxJywuNoYpY/ry4g2nUry3nEuf+pL3VxS7Hcs0IisWxphGMzKzA+/dei69O6Twq1eX8KfZq6isrnU7lmkEViyMMY0qPTWZ6T8/k/8+uwcvfZ3Hlf9YSKHduxT2rFgYYxpdQlwMf7y0H3+7Zigbd+xn3JNf8Ona7W7HMifAioUxJmguOqUz795yDp1bJfPfL2Xzvx+upbrGTkuFIysWxpig6t6uOW//6iwmn9qVZxds5Jrnv2XHPt99TZnQZcXCGBN0SfGxPHTFQB6dNIjlBXu5+Mkv+XrjTrdjmWNgxcIY02SuGNaFd24+m1bJcVz7/Lc8/ekGamsj416vSGfFwhjTpPp0bMHsm8/hkoFpPPLRem54aRG7D1S6Hcv4YcXCGNPkmifG8cTkwTwwYQALN+7ikie/YPGWPW7HMg2wYmGMcYWIcO0Z3Xjrl2cRGytc9Y+F/PPLzURKF0SRxoqFMcZVp3RpxZybz2Vk3w7cP2c1v/z3EvZVHDmMq3GXFQtjjOtaNYvnuZ8M466LT+bjNdu59KkvWVW01+1YxosVC2NMSBAR/t/wnrxx4xkcqqrlR89+zWvfbbXTUiHCioUxJqRkdW/De7eew+k92jB15gp+M30ZBytt6Fa3WbEwxoSctimJvHTDadwxug9vLy1k/NNfkbvDhm51kw1+ZIwJaV9u2Mltr+dQXlXDFUPT+XRtiQ2D3Ihs8CNjTEQ4J6Md7916Lh1bJvLKN1spLC1HgcLScqbOXMGsnEK3I0YFKxbGmJDXqVUSh3wMolReVcO0uetcSBR9rFgYY8JCcanvnmoLS8uZt3q7jcgXZHFuBzDGmECkpSb7HHEvRuBn/8omtVk8407pzI+GpDOsW2tExIWUkcuKhTEmLEwZk8nUmSsor6r5flpyfCwPTOhParMEZi0t4q0lBbz67Va6tE5m/OA0JgxOJ6NjCxdTRw4rFsaYsFB31dO0uet8Xg11/skd2X+omrkrtzFraSF/W7CRZ+ZvpH9aSyYMTueywWl0bJnk5rcQ1uzSWWNMRNpRVsGcZcXMWlrI8oK9iMBZvdoyfnA6Ywd0omVSvNsRQ0Kgl85asTDGRLyNJft5Z2kRs3IK2br7IAlxMYw+uQMTBqdzXmYHEuKi91ofKxbGGFOPqpKTX8o7OYXMWV7MrgOVtEqO52KnYTyrW2tiYqKrYdyKhTHGNKCqppYvN+xk1tJCPlq1nfKqGtJTk7nMaRjP7BQdDeNWLIwxJkAHDlXz8ertvJ1TyJe5O6mpVU7u3JIJg9O4bHAanVslux0xaKxYGGPMcSgpO8R7y4t4e2kRy/JLEYHTe7ThR0PSGTugM62S45mVU3jUq7LCjRULY4w5QZt3HuCdpYW8s7SIzTsPkBAXQ9+OKazdVkZlzQ+fncnxsTx4+SlhWTCsWBhjTCNRVZYV7GVWTiH/WphHrY+PzfYtEvnkNyPC7pJcKxbGGBMEPe58j4Y+Nds2T6Bb22Z0b9ec7m2b071dc3q0bU63ds1CspAEWizsDm5jjDkGR+ujqk3zeG4c3ou8nQfI23WAr3N3MXPJ4d2n+yok3Z3XoVhIvFmxMMaYY3C0Pqr+eEn/I9osyitr2LL7AHk7D5K36wBbdh1g884DLNx4ZCFp0zzBUzjqikgAhaQpG9qtWBhjzDHw10eVt+SEWPp2aknfTi2PmFdeWcPW3QfZvNNTRPJ2eYrKwk27mJnTcCHp1rYZW3Yd4NkFG6mo8nTNXjcYlHfGxhTUNgsRGQs8AcQCz6vqQ/XmJwL/AoYBu4CrVDXPmTcV+ClQA9yqqnMbei9rszDGRIqKqhq27DqykOTtOkDxXt/jetRJT03mqztHBfxerrdZiEgs8AxwAVAALBKR2aq62muxnwJ7VLW3iEwGHgauEpF+wGSgP5AGzBORPqpagzHGRLik+FgyO7XweRd5XSEZ8/jnPtct8tGe0hiC2XvWaUCuqm5S1UrgdWB8vWXGAy87z98EzhfPiCXjgddV9ZCqbgZyne0ZY0xUqysk6am+7ypPO8r0ExXMYpEO5Hu9LnCm+VxGVauBvUDbANdFRG4UkWwRyS4pKWnE6MYYE9qmjMkkOT72sGnJ8bFMGZMZlPcLZrHw1XVj/QaSoy0TyLqo6nOqmqWqWe3btz+OiMYYE54mDEnnwctPIT01GcHTVhHMu8iDeTVUAdDV63UXoOgoyxSISBzQCtgd4LrGGBPVJgxJb7IuRoJ5ZLEIyBCRHiKSgKfBena9ZWYD1znPJwKfqufyrNnAZBFJFJEeQAbwXRCzGmOMaUDQjixUtVpEbgbm4rl09gVVXSUi9wHZqjob+Cfwiojk4jmimOysu0pEpgOrgWrgJrsSyhhj3GN9QxljTBQL9D6L6B141hhjTMCsWBhjjPErYk5DiUgJsOUENtEO2NlIccKd7YvD2f44nO2PH0TCvuimqn7vPYiYYnGiRCQ7kPN20cD2xeFsfxzO9scPomlf2GkoY4wxflmxMMYY45cVix8853aAEGL74nC2Pw5n++MHUbMvrM3CGGOMX3ZkYYwxxi8rFsYYY/yK+mIhImNFZJ2I5IrInW7ncZOIdBWR+SKyRkRWichtbmdym4jEikiOiMxxO4vbRCRVRN4UkbXO78iZbmdyk4jc4fydrBSR10Qkye1MwRTVxcJr6NeLgH7A1c6QrtGqGviNqp4MnAHcFOX7A+A2YI3bIULEE8CHqtoXGEQU7xcRSQduBbJUdQCezlInu5squKK6WBDY0K9RQ1WLVXWJ87wMz4dB03SWH4JEpAswDnje7SxuE5GWwHA8PUWjqpWqWupuKtfFAcnOWDzNiPAxd6K9WAQ0fGs0EpHuwBDgW3eTuOpx4HdArdtBQkBPoAR40Tkt97yINHc7lFtUtRB4BNgKFAN7VfUjd1MFV7QXi4CGb402IpICvAXcrqr73M7jBhG5BNihqovdzhIi4oChwN9UdQhwAIjaNj4RaY3nLEQPIA1oLiLXupsquKK9WNjwrfWISDyeQvGqqs50O4+LzgYuE5E8PKcnR4nIv92N5KoCoEBV644038RTPKLVaGCzqpaoahUwEzjL5UxBFe3FIpChX6OGiAiec9JrVPWvbudxk6pOVdUuqtodz+/Fp6oa0f85NkRVtwH5IpLpTDofz0iW0WorcIaINHP+bs4nwhv8gzasajg42tCvLsdy09nAT4AVIrLUmfYHVX3fxUwmdNwCvOr8Y7UJuMHlPK5R1W9F5E1gCZ6rCHOI8K4/rLsPY4wxfkX7aShjjDEBsGJhjDHGLysWxhhj/LJiYYwxxi8rFsYYY/yyYmG+JyIqIo96vf6tiPypkbb9kohMbIxt+XmfSU6PqPPrTe8uIuUistTr8V/BzuMjX+cT6cFWRP5wHOv43CfOvA9FpLR+Jufeo29FZIOIvOFcLouIJDqvc5353X1ss7uI/LiBPGnOZacNZe4uIisbmJ8gIp87/TKZJmDFwng7BFwuIu3cDuLN6R04UD8FfqWqI33M26iqg70e//L3XoG+9zF8aP0a+L8Al/XlmIsFDe+TaXjuranvYeAxVc0A9jjbqNvWHlXtDTzmLFdfd8BnsRCROFUtUtUT+sfB6fjzE+CqE9mOCZwVC+OtGs+NRXfUn1H/yEBE9jtfzxORz0RkuoisF5GHROQaEflORFaISC+vzYwWkS+c5S5x1o8VkWkiskhElovIz722O19E/gOs8JHnamf7K0XkYWfaH4FzgL+LyLRAv2kR2S8i94nIt8CZIpInIn8UkS+BSSIyWES+cfK97fQLhIgsEJG/iMhnwG3Of/ArRWSZiHx+lLe7AvjQWT9JRF50vo8cERnpTL9eRJ72yjfH2R8P4enldKmIvNoY+0RVPwHK6m1HgFF4uvQAeBmY4Dwf77zGmX++s7y3h4BznZx3ON/PDBF5F/jI+6jBef6FiCxxHkd0mSEi/Z3fp6XOzyDDmTULuObIXWyCQlXtYQ9UFWA/0BLIA1oBvwX+5Mx7CZjovazz9TygFOgMJAKFwP84824DHvda/0M8/6Bk4OlrKAm4EbjbWSYRyMbTOdt5eDqr6+EjZxqe7hba4+mF4FNggjNvAZ4xBuqv0x0oB5Z6Pc515ilwpdeyecDvvF4vB0Y4z+/z+p4WAM96LbcCSHeep/rI0ANY7PX6N8CLzvO+zveUBFwPPO213BzgPO/93hj7xGvd84A5Xq/b4em6v+51V2Cl83wl0MVr3kagnZ/tXe/8vNt4/SzqttcMSHKeZwDZPpZ5CrjGeZ4AJDvPY4ESt/9uouVh5/vMYVR1n4j8C8/ALuUBrrZIVYsBRGQjUNdV8wrA+9THdFWtBTaIyCY8H5AXAgO9jlpa4fnQqAS+U9XNPt7vVGCBqpY47/kqnrEWZvnJuVFVB/uYXoOn80RvbzjbboXng/8zZ/rLwIz6yzm+Al4Skel4OparrzOebr7rnIPngxBVXSsiW4A+fr6HoznefeJLQ70xH29PzR+r6m4f0+OBp0VkMJ6fg6/vfyFwl3jGF5mpqhsAVLVGRCpFpIV6xl8xQWSnoYwvj+M5N+09XkE1zu+Lc9ohwWveIa/ntV6vazm8/7H6HyqK58PnFv2hHaGH/jAuwIGj5PP1gXUiKlS1pt60o713fd8vp6q/AO7G85/4UhFpW2/ZcjxHDnWO9n18v68dgQzX2Zj7ZCeQ6tUO490b8/c9NTvzWwG+ikB9R9ufdwDb8Yy8l8Xhv1cAqOp/gMvw7L+5IjLKa3YiUBHA+5sTZMXCHMH5D3A6PzRqgufUzDDn+Xg8/xEeq0kiEuO0Y/QE1uHpxPGX4ukaHRHpI/4H1fkWGCEi7ZwG6KuBz/ysc1xUdS+wR0TOdSb95GjvJSK9VPVbVf0jng/crvUWWY/n9Eqdz3HOuYtIH+AkPPskDxjs7KuueEZ0rFNVt6/qabR9op5zPPOBuqO964B3nOezndc48z91lvdWBrQI8O1aAcXOEedP8JxaOoyI9AQ2qeqTzvsPdKa3xXMaqirA9zInwE5DmaN5FLjZ6/X/Ae+IyHd4rkIJ9D9vb+vwfIB1BH6hqhUi8jyeD9AlzhFLCT80pvqkqsUiMhXPB5oA76vqOw2t4+glP/SmC55ehp8MYL3r8DQQN6Ph3lanOY2vgmcfLauX+4CIbBSR3qqaCzzrbHcFnqOJ61X1kIh8BWzGcxpvJZ6eTes8BywXkSWqeo3Xto9rn4jIF3hOB6aISAHwU1WdC/weeF1EHsDTo+o/nVX+CbwiIrl4jih8jTu9HKgWkWV42qr2NBDhWeAtEZnkZPf1e3UVcK2IVAHb8LQbgecUp/WI3ESs11ljmpCI/AgYpqp3u50l3InITGCqqq5zO0s0sCMLY5qQqr7toy3DHCPx3CQ4ywpF07EjC2OMMX5ZA7cxxhi/rFgYY4zxy4qFMcYYv6xYGGOM8cuKhTHGGL/+Pzam8ogx6k+XAAAAAElFTkSuQmCC\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 35,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data = stats.poisson.rvs(mu=3, loc=0, size=100)\n",
        "print(\"Mean: %f\" % np.mean(data))\n",
        "print(\"Standard Deviation: %f\" % np.std(data, ddof=1))\n",
        "\n",
        "plt.hist(data, bins = 9, normed = True)\n",
        "plt.xlim(0,10)\n",
        "plt.xlabel('Number of Errors (out of 100 trials)')\n",
        "plt.title('Simulating Poisson Random Variables')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean: 3.000000\n",
            "Standard Deviation: 1.758098\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 36,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Beta Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = alpha\n",
        "beta = beta\n",
        "x = np.arange(0, 1, 0.01)\n",
        "y = stats.beta.pdf(x, alpha, beta)\n",
        "plt.plot(x, y)\n",
        "plt.title('Beta Distribution: alpha=%.1f, beta=%.1f' % (alpha,beta))\n",
        "plt.xlabel('Range')\n",
        "plt.ylabel('Probability density')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 37,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Exponential Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "lambd = 0.5 # lambda\n",
        "x = np.arange(0, 1, 0.01)\n",
        "y = lambd * np.exp(-lambd * x)\n",
        "plt.plot(x, y)\n",
        "plt.title('Exponential: $lambda\\$ = %.2f' % lambd)\n",
        "plt.xlabel(\"Range\")\n",
        "plt.ylabel(\"Probability density\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 38,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Lognormal Distribution "
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import lognorm\n",
        "\n",
        "s = np.random.lognormal(mu, sigma, 1000)\n",
        "\n",
        "count, bins, ignored = plt.hist(s, 100, normed=True, align='mid')\n",
        "x = np.linspace(min(bins), max(bins), 10000)\n",
        "pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) / (x * sigma * np.sqrt(2 * np.pi)))\n",
        "\n",
        "plt.plot(x, pdf, linewidth=2, color='r')\n",
        "plt.xlabel('Range')\n",
        "plt.ylabel('Probability')\n",
        "plt.axis('tight')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 39,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Calculate Quantile"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Quatile \n",
        "# 5% quantile\n",
        "print('5% quantile ', norm.ppf(0.05, mu, sigma))\n",
        "# 95% quantile\n",
        "print('95% quantile ', norm.ppf(0.95, mu, sigma))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5% quantile  -1.02188692209\n",
            "95% quantile  1.02582945005\n"
          ]
        }
      ],
      "execution_count": 40,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Calcuate the 25% and 75% Quantile of the stock's returns\n",
        "# 25% quantile\n",
        "q25 = norm.ppf(0.25, mu, sigma)\n",
        "print('25% quantile ', q25)\n",
        "# 75% quantile\n",
        "q75 = norm.ppf(0.75, mu, sigma) \n",
        "print('75% quantile ', q75)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "25% quantile  -0.417872691034\n",
            "75% quantile  0.421815218993\n"
          ]
        }
      ],
      "execution_count": 41,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Statistical Hypothesis Tests"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Hypothesis test is a statistical method that is used to make statistical decisions for experimental data. In addition, is used for to compare two dataset. \n",
        "\n",
        "Statistical tests is used to check if the data has a Gaussian distribution or not\n",
        "\n",
        "Alpha or α: is the probability of rejecting the null hypothesis when it is true.\n",
        "\n",
        "P-values: the probability of obtaining an effect at least as extreme as the one in the sample data while assuming the truth of the null hypothesis.\n",
        "\n",
        "p-value <= alpha: reject H0, not normal.\n",
        "\n",
        "p-value > alpha: fail to reject H0, normal."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Calculate test Statistics"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# https://www.statisticshowto.datasciencecentral.com/standardized-test-statistic/\n",
        "mu = df['Returns'].mean()\n",
        "sigma = df['Returns'].std(ddof=1)\n",
        "n = df['Returns'].shape[0]\n",
        "\n",
        "# if sample size n is large enough, we can use z-distribution, instead of t-distribtuion\n",
        "# mu = 0 under the null hypothesis\n",
        "zhat = (mu - 0)/(sigma/n**0.5)\n",
        "print(zhat)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.782379363617273\n"
          ]
        }
      ],
      "execution_count": 42,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Set decision criteria"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# confidence level\n",
        "alpha = 0.05\n",
        "\n",
        "zleft = norm.ppf(alpha/2, 0, 1)\n",
        "zright = -zleft  # z-distribution is symmetric \n",
        "print(zleft, zright)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-1.95996398454 1.95996398454\n"
          ]
        }
      ],
      "execution_count": 43,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Decision to reject H0 or not"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "print('At significant level of {}, shall we reject: {}'.format(alpha, zhat>zright or zhat<zleft))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "At significant level of 0.05, shall we reject: False\n"
          ]
        }
      ],
      "execution_count": 44,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## One Tail Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Test one tail\n",
        "mu = df['Returns'].mean()\n",
        "sigma = df['Returns'].std(ddof=1)\n",
        "n = df['Returns'].shape[0]\n",
        "\n",
        "# if sample size n is large enough, we can use z-distribution, instead of t-distribtuion\n",
        "# mu = 0 under the null hypothesis\n",
        "zhat = (mu - 0)/(sigma/n**0.5)\n",
        "print(zhat)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.782379363617273\n"
          ]
        }
      ],
      "execution_count": 45,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = 0.05\n",
        "\n",
        "zright = norm.ppf(1-alpha, 0, 1)\n",
        "print(zright)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.64485362695\n"
          ]
        }
      ],
      "execution_count": 46,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('At significant level of {}, shall we reject: {}'.format(alpha, zhat>zright))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "At significant level of 0.05, shall we reject: True\n"
          ]
        }
      ],
      "execution_count": 47,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Test for p-value"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "p_value = 1 - norm.cdf(zhat, 0, 1)\n",
        "print(p_value)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.0373436942162\n"
          ]
        }
      ],
      "execution_count": 48,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('At significant level of {}, shall we reject: {}'.format(alpha, p_value < alpha))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "At significant level of 0.05, shall we reject: True\n"
          ]
        }
      ],
      "execution_count": 49,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The stock data is continuous data. Here the list of doing hypothesis test.\n",
        "\n",
        "For this part, is about comparing features and targets or two samples. Some of the hypothesis testing, we can test one samples.\n",
        "\n",
        "List of continuous: https://docs.scipy.org/doc/scipy/reference/tutorial/stats/continuous.html"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Shapiro-Wilk Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Shapiro-Wilk Test\n",
        "from scipy.stats import shapiro\n",
        "import scipy as sp\n",
        "\n",
        "\n",
        "W_test, p_value = shapiro(df['Returns'])"
      ],
      "outputs": [],
      "execution_count": 50,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# confidence level is 95%, that is, alpha=0.05\n",
        "print('Shapiro-Wilk Test')\n",
        "print('-'*40)\n",
        "\n",
        "alpha = 0.05\n",
        "if p_value < alpha:  # null hypothesis: x comes from a normal distribution\n",
        "    print(\"H0: the sample has a Gaussian distribution.\")\n",
        "    print(\"The null hypothesis can be rejected\")\n",
        "else:\n",
        "    print(\"H1: the sample does not have a Gaussian distribution.\")\n",
        "    print(\"The null hypothesis cannot be rejected\")"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Shapiro-Wilk Test\n",
            "----------------------------------------\n",
            "H0: the sample has a Gaussian distribution.\n",
            "The null hypothesis can be rejected\n"
          ]
        }
      ],
      "execution_count": 51,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## D’Agostino’s K^2 Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Anderson_Darling Test\n",
        "from scipy.stats import anderson\n",
        "\n",
        "result = anderson(df['Returns'].dropna())\n",
        "result"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 52,
          "data": {
            "text/plain": [
              "AndersonResult(statistic=24.987609879932279, critical_values=array([ 0.574,  0.654,  0.785,  0.915,  1.089]), significance_level=array([ 15. ,  10. ,   5. ,   2.5,   1. ]))"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 52,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('D’Agostino’s K^2 Test')\n",
        "print('-'*40)\n",
        "print('Statistic: %.3f' % result.statistic)\n",
        "p = 0\n",
        "for i in range(len(result.critical_values)):\n",
        "\tsl, cv = result.significance_level[i], result.critical_values[i]\n",
        "\tif result.statistic < result.critical_values[i]:\n",
        "\t\tprint('%.3f: %.3f, data looks normal (fail to reject H0)' % (sl, cv))\n",
        "\telse:\n",
        "\t\tprint('%.3f: %.3f, data does not look normal (reject H0)' % (sl, cv))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "D’Agostino’s K^2 Test\n",
            "----------------------------------------\n",
            "Statistic: 24.988\n",
            "15.000: 0.574, data does not look normal (reject H0)\n",
            "10.000: 0.654, data does not look normal (reject H0)\n",
            "5.000: 0.785, data does not look normal (reject H0)\n",
            "2.500: 0.915, data does not look normal (reject H0)\n",
            "1.000: 1.089, data does not look normal (reject H0)\n"
          ]
        }
      ],
      "execution_count": 53,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The correlation is used to test out the samples or features is correlation or not.\n",
        "\n",
        "Therefore, to check two samples or features are related or not."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## F-test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy\n",
        "from scipy.stats import f\n",
        "\n",
        "F = df['Adj Close'].var() / df['Returns'].var()\n",
        "df1 = len(df['Adj Close']) - 1 \n",
        "df2 = len(df['Returns']) - 1 \n",
        "p_value = scipy.stats.f.cdf(F, df1, df2)"
      ],
      "outputs": [],
      "execution_count": 54,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('F-test')\n",
        "print('-'*40)\n",
        "print('Statistic: %.3f' % p_value)\n",
        "# interpret the significance\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('H0: the two samples are independent. p=%.3f' % p_value)\n",
        "else:\n",
        "\tprint('H1: there is a dependency between the samples. p=%.3f' % p_value)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "F-test\n",
            "----------------------------------------\n",
            "Statistic: 1.000\n",
            "H0: the two samples are independent. p=1.000\n"
          ]
        }
      ],
      "execution_count": 55,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Pearson’s Correlation Coefficient"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import pearsonr\n",
        "\n",
        "coef, p_value = pearsonr(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 56,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Pearson’s Correlation Coefficient')\n",
        "print('-'*40)\n",
        "print('Correlation Test: %.3f' % coef)\n",
        "# interpret the significance\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('H0: the two samples are independent. p=%.3f' % p_value)\n",
        "else:\n",
        "\tprint('H1: there is a dependency between the samples. p=%.3f' % p_value)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Pearson’s Correlation Coefficient\n",
            "----------------------------------------\n",
            "Correlation Test: 0.998\n",
            "H1: there is a dependency between the samples. p=0.000\n"
          ]
        }
      ],
      "execution_count": 57,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Spearman's Rank Correlation"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Spearman's Rank Correlation\n",
        "from scipy.stats import spearmanr\n",
        "\n",
        "coef, p_value = spearmanr(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 58,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Spearman’s Rank Correlation')\n",
        "print('-'*40)\n",
        "print('Spearmans correlation coefficient: %.3f' % coef)\n",
        "# interpret the significance\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Samples are uncorrelated (fail to reject H0) p=%.3f' % p_value)\n",
        "else:\n",
        "\tprint('Samples are correlated (reject H0) p=%.3f' % p_value)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Spearman’s Rank Correlation\n",
            "----------------------------------------\n",
            "Spearmans correlation coefficient: 0.998\n",
            "Samples are correlated (reject H0) p=0.000\n"
          ]
        }
      ],
      "execution_count": 59,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Kendall's Rank Correlation"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Kendall's Rank Correlation\n",
        "from scipy.stats import kendalltau\n",
        "\n",
        "coef, p_value = kendalltau(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 60,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Kendall’s Rank Correlation')\n",
        "print('-'*40)\n",
        "print('Kendall correlation coefficient: %.3f' % coef)\n",
        "# interpret the significance\n",
        "alpha = 0.05\n",
        "if p > alpha:\n",
        "\tprint('Samples are uncorrelated (fail to reject H0) p=%.3f' % p_value)\n",
        "else:\n",
        "\tprint('Samples are correlated (reject H0) p=%.3f' % p_value)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Kendall’s Rank Correlation\n",
            "----------------------------------------\n",
            "Kendall correlation coefficient: 0.967\n",
            "Samples are correlated (reject H0) p=0.000\n"
          ]
        }
      ],
      "execution_count": 61,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Chi-Squared Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Chi-Squared Test\n",
        "from scipy.stats import chi2_contingency\n",
        "from scipy.stats import chi2\n",
        "\n",
        "stat, p_value, dof, expected = chi2_contingency(df[['Open','Low','High','Adj Close','Volume']])"
      ],
      "outputs": [],
      "execution_count": 62,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# interpret test-statistic\n",
        "print('Chi-Squared Test')\n",
        "print('-'*40)\n",
        "\n",
        "prob = 0.95\n",
        "critical = chi2.ppf(prob, dof)\n",
        "if abs(stat) >= critical:\n",
        "\tprint('Dependent (reject H0)')\n",
        "else:\n",
        "\tprint('Independent (fail to reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Chi-Squared Test\n",
            "----------------------------------------\n",
            "Dependent (reject H0)\n"
          ]
        }
      ],
      "execution_count": 63,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# interpret p-value\n",
        "alpha = 1.0 - prob\n",
        "if p_value <= alpha:\n",
        "\tprint('Dependent (reject H0)')\n",
        "else:\n",
        "\tprint('Independent (fail to reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Dependent (reject H0)\n"
          ]
        }
      ],
      "execution_count": 64,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('dof=%d' % dof)\n",
        "print(expected)\n",
        "# interpret test-statistic\n",
        "prob = 0.95\n",
        "critical = chi2.ppf(prob, dof)\n",
        "print('probability=%.3f, critical=%.3f, stat=%.3f' % (prob, critical, stat))\n",
        "if abs(stat) >= critical:\n",
        "\tprint('Dependent (reject H0)')\n",
        "else:\n",
        "\tprint('Independent (fail to reject H0)')\n",
        "# interpret p-value\n",
        "alpha = 1.0 - prob\n",
        "print('significance=%.3f, p=%.3f' % (alpha, p_value))\n",
        "if p <= alpha:\n",
        "\tprint('Dependent (reject H0)')\n",
        "else:\n",
        "\tprint('Independent (fail to reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "dof=5024\n",
            "[[  4.29482020e+00   4.19128857e+00   4.39401482e+00   4.29387501e+00\n",
            "    2.28871987e+07]\n",
            " [  7.95610731e+00   7.76431610e+00   8.13986425e+00   7.95435634e+00\n",
            "    4.23982845e+07]\n",
            " [  8.05627575e+00   7.86206987e+00   8.24234622e+00   8.05450274e+00\n",
            "    4.29320845e+07]\n",
            " ..., \n",
            " [  2.08993226e+01   2.03955201e+01   2.13820204e+01   2.08947231e+01\n",
            "    1.11372986e+08]\n",
            " [  2.04942584e+01   2.00002205e+01   2.09676007e+01   2.04897480e+01\n",
            "    1.09214389e+08]\n",
            " [  1.59001374e+01   1.55168462e+01   1.62673724e+01   1.58966382e+01\n",
            "    8.47322094e+07]]\n",
            "probability=0.950, critical=5190.009, stat=14246523.362\n",
            "Dependent (reject H0)\n",
            "significance=0.050, p=0.000\n",
            "Dependent (reject H0)\n"
          ]
        }
      ],
      "execution_count": 65,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This part is to compare two samples or features; as a results, to check if they both independent samples."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Parametric Statistical Hypothesis Tests"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "T-test for the means of two independent samples of scores Two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Parametric Statistical Hypothesis Tests\n",
        "# Student’s t-test\n",
        "from scipy.stats import ttest_ind\n",
        "\n",
        "stat, p_value = ttest_ind(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 66,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Paired Students t-Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Paired Students t-Test\n",
            "----------------------------------------\n",
            "Statistics=0.007, p=0.994\n",
            "Same distributions (fail to reject H0)\n"
          ]
        }
      ],
      "execution_count": 67,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Paired Student’s t-test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Paired Student’s t-test\n",
        "from scipy.stats import ttest_rel\n",
        "\n",
        "stat, p_value = ttest_rel(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 68,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Paired Students t-Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Paired Students t-Test\n",
            "----------------------------------------\n",
            "Statistics=0.171, p=0.000\n",
            "Same distributions (fail to reject H0)\n"
          ]
        }
      ],
      "execution_count": 69,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Analysis of Variance Test (ANOVA)"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Analysis of Variance Test (ANOVA)\n",
        "from scipy.stats import f_oneway\n",
        "\n",
        "stat, p_value = f_oneway(df['Open'], df['Adj Close'], df['Volume'])"
      ],
      "outputs": [],
      "execution_count": 70,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Analysis of Variance Test (ANOVA)')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Analysis of Variance Test (ANOVA)\n",
            "----------------------------------------\n",
            "Statistics=1424.935, p=0.000\n",
            "Different distributions (reject H0)\n"
          ]
        }
      ],
      "execution_count": 71,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Mann-Whitney U Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Nonparametric Statistical Hypothesis Tests\n",
        "# Mann-Whitney U Test\n",
        "from scipy.stats import mannwhitneyu\n",
        "\n",
        "stat, p_value = mannwhitneyu(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 72,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Mann-Whitney U Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distribution (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distribution (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mann-Whitney U Test\n",
            "----------------------------------------\n",
            "Statistics=789756.500, p=0.494\n",
            "Same distribution (fail to reject H0)\n"
          ]
        }
      ],
      "execution_count": 73,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Wilcoxon Signed-Rank Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Wilcoxon Signed-Rank Test\n",
        "from scipy.stats import wilcoxon\n",
        "\n",
        "stat, p_value = wilcoxon(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 74,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Wilcoxon Signed-Rank Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distribution (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distribution (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Wilcoxon Signed-Rank Test\n",
            "----------------------------------------\n",
            "Statistics=364609.000, p=0.849\n",
            "Same distribution (fail to reject H0)\n"
          ]
        }
      ],
      "execution_count": 75,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Kruskal-Wallis Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Kruskal-Wallis Test\n",
        "from scipy.stats import kruskal\n",
        "\n",
        "stat, p_value = kruskal(df['Open'], df['Adj Close'], df['Volume'])"
      ],
      "outputs": [],
      "execution_count": 76,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Kruskal-Wallis Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Kruskal-Wallis Test\n",
            "----------------------------------------\n",
            "Statistics=2505.346, p=0.000\n",
            "Different distributions (reject H0)\n"
          ]
        }
      ],
      "execution_count": 77,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Friedman Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import friedmanchisquare\n",
        "\n",
        "stat, p_value = friedmanchisquare(df['Open'], df['Adj Close'], df['Volume'])"
      ],
      "outputs": [],
      "execution_count": 78,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Friedman Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Friedman Test\n",
            "----------------------------------------\n",
            "Statistics=1897.004, p=0.000\n",
            "Different distributions (reject H0)\n"
          ]
        }
      ],
      "execution_count": 79,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Levene Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Levene Test\n",
        "from scipy.stats import levene\n",
        "\n",
        "stat, p_value = levene(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 80,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Levene Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Levene Test\n",
            "----------------------------------------\n",
            "Statistics=0.000, p=0.983\n",
            "Same distributions (fail to reject H0)\n"
          ]
        }
      ],
      "execution_count": 81,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Mood's Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import mood\n",
        "\n",
        "stat, p_value = mood(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 82,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Mood Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mood Test\n",
            "----------------------------------------\n",
            "Statistics=0.005, p=0.996\n",
            "Same distributions (fail to reject H0)\n"
          ]
        }
      ],
      "execution_count": 83,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Mood’s median test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import median_test\n",
        "\n",
        "stat, p_value, med, tbl = median_test(df['Open'], df['Adj Close'], df['Volume'])"
      ],
      "outputs": [],
      "execution_count": 84,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Mood’s median test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mood’s median test\n",
            "----------------------------------------\n",
            "Statistics=1880.581, p=0.000\n",
            "Different distributions (reject H0)\n"
          ]
        }
      ],
      "execution_count": 85,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "stat, p_value, med, tbl = median_test(df['Open'], df['Adj Close'], df['Volume'],lambda_=\"log-likelihood\")"
      ],
      "outputs": [],
      "execution_count": 86,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Mood’s median test with lambda')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mood’s median test with lambda\n",
            "----------------------------------------\n",
            "Statistics=2383.028, p=0.000\n",
            "Different distributions (reject H0)\n"
          ]
        }
      ],
      "execution_count": 87,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Kolmogorov-Smirnov Test"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Kolmogorov-Smirnov test\n",
        "from scipy.stats import ks_2samp\n",
        "\n",
        "stat, p_value = ks_2samp(df['Open'], df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 88,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Kolmogorov-Smirnov Test')\n",
        "print('-'*40)\n",
        "print('Statistics=%.3f, p=%.3f' % (stat, p_value))\n",
        "# interpret\n",
        "alpha = 0.05\n",
        "if p_value > alpha:\n",
        "\tprint('Same distributions (fail to reject H0)')\n",
        "else:\n",
        "\tprint('Different distributions (reject H0)')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Kolmogorov-Smirnov Test\n",
            "----------------------------------------\n",
            "Statistics=0.006, p=1.000\n",
            "Same distributions (fail to reject H0)\n"
          ]
        }
      ],
      "execution_count": 89,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Box-Cox Power Transformation"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import boxcox\n",
        "\n",
        "df['boxcox'], lam = boxcox(df['Adj Close'])"
      ],
      "outputs": [],
      "execution_count": 90,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Lambda: %f' % lam)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Lambda: -0.119624\n"
          ]
        }
      ],
      "execution_count": 91,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot line\n",
        "plt.title('Stock Box-Cox Power Transformation')\n",
        "plt.plot(df['boxcox'])\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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PGWOeb73fGFNtjKm1l18GXCJS0Po4pZRKRlsPhebLX7t5LmdOKorqscFpmTMmFXH7gsmB9UFZqYwpyOL/zR4FQFFOOtvLakJGk4yXaFrLCPAosNkYc187xwyxj0NEZtnnPRLLgiqlVLyU17S0UZ88JIeJg9tOztGe4LRMeoqD684Yxys3nc6TX58d2P6VOaMBGDUok0sefI+7XtwUg1JHFk2XqVOBrwKfiMg6e9uPgFEAxpiHgcuAb4mIB2gALjfJNueUUkq1o67JA8DIQRm8cP2pnXqsK6jmnmb3aJ08JBeGhB6TmuLgX2tLqGv2MrN4UOvTxFyHwd0YsxyQDo55EHgwVoVSSqme5PFaddFF35gTcfz2cIKDe1aEHq3jCrPZfMC6XTl7TPyDu/ZQVUr1e/6JNlIjNGtsj9PRUveN1KM1+GZrUW56p5+nszS4K6X6jaVbyvjPuv1ttvvbn0dqsx6N7AjB3R/4Jw+JPp/fHToqpFKq37j6iVUAXDKjpR/mva9s4cmV1iBfwTdHOyMtxUGTx8fgCDVyh9XmhItnDOvSc3SWBnelVL/Qenz1fRX1nP6rpSHbXF2suT/zzZNZvL6UguzUdo+ZN7mINzYf6lLqpys0uCul+oWngobgbWj28se32/YW7Wpwnz5yYMhQA+FcMWskeZkuzpjUMx04NbgrpfqFt7aUBZbLa5rYV9HQ5pjgm6OxJiIsOHZo3M7fmgZ3pVSft7O8lk2lLaOmPP3hXmqaPJw+oYC/f302nx6s4f0dhxNYwtjT1jJKqT5v3m+XUVbTxGnjrVFRHl62g4q6pkDrlklDclh46phEFjHmNLgr1Yt4vD7+8MY2qurdiS5Kr/S104oDy/sqGiK2buntNLgr1Yu8uvEQv3tjK5f+8b1EF6VXmjEyL2Q9zdV3Q2DfvTKl+qAj9iTMuw7XhWxvaPayZk9shpPdV1HPRQ8s53BtU8cH9wLB33LyMl189NP5gfVvzh2XiCL1CL2hqlQvUtPoCVk/WNVIbZOH659ay6eHanjje3MZXxR9D8i9R+opyEklM7UlFPz53Z18sr+KF9eX9ok89Ar7Rumfr5yJiJCXlcruey5IcKniT4O7Ur3Ir1/9NLD88/9u4rH3doXs31haHXVwN8Yw99dLmTFyIC9cfyoPLd3OR3sryYgw+FV73F4fd7+0maoGNyJw58XHkJvu6vR54mF9SRWpTgdn9lD78mShwV2pXqLZ0zLBw7AB6W0CO8C6fZUhXesjqbTTFev2VXKwqjHkgwPA44t+1O63tpTxxIrdgfUF04Yyf+rgqB8fT1UNbnIzXF3uoNRb9a+rVaoX21bWMltQaVVjhCOjU9XQkovefaSuzf7fvb6VSNMyvLLhYCD3v72sNmRfRieHzQ22du9RVsdwOrpFH+7tM/cPOkODu1JJ7pIHl1N8+0vc8sx6AE4cndfusS99fACA59aUUHz7S8z7zdvtHtsU9E1gZ3nb4F7X7GXJhoPtPv66J9dw1m/exuczfHqwhqED0rnwOKsHptvX9WnkPvfHFVz28PtdfnywNzcfisl5eiMN7kolufUlVQBsOWjV3KcMDc2p//5LM1jzk3MAKKtpwuP18f1nrQ+CnYfbBm2/4DTPS5+Uhux79rqTAfj2U2sDE0wAgZp88BygZ9+3jMXrSxlflB1ofeKf/KKzfJ1IBUXjW0+tBWDhKcUxPW9voDl3pXoZ/7jgBdmprPrxOdjTFwf84c1tUZ2n2esNLL+33ZryePvdC/D4DGkpLfW+ZVvLKc7PosnjZfYv3uSOi6Yyb3LL5NH+1MwXZo4kxR4y19PFCaBXxTAdU93oDnyA+Seo7k+05q5Ukhs6IJ2LpltjgI8pyGJwjtWrct7kopDAvv6OcwF44K2W0Q6HDWjbA/NoXTN3Lt7YplklWJNVpLuciAjfnTcegHuWbOFbT61hY2k1TR4fP/73BpZvaxmHxSEwbXguF08fFhgP3d2FGnizx8eXHlkZWO/uNMwXPbAcgF9ddlynJrzuKzS4K5XkKuqaGTognccXnsQz3zyZq04pZtkPzuSXnzsu5LgBmS4GZbWMJ/7FmSPwGThc20Tx7S+xbGs5AL99/VOeWLGb59aUhDz+/GOHhKx/b/7EwPLbn5ZTXtNyU/Kv7+8OLPsMHDfCGu42xWGFlK7U3NftqwxZb+5i7R+gtsnDniP1TCjK5tIoWw/1NRrclUpiDc1emjw+8jJTOWtyEYU5aTgdwuj8rLDD01bUNQPw1DWzcToErzF8YufsH1u+yz6nFTQb3aHzhhbnZ4Wcq3W656Z/rgssb9hfTX7QB4k/gLakZTpf6/6/ZTtC1huarbTR3iP1zL9vGXuP1Ed9rk/t+xO3nTeZ1JT+Geb651Ur1Utssm9mZqd37vbYzOI8HCIYYzBYgdYfq/3pjga3lZaZMy4faJkGLlqDslIZW5jFj8+fwqwxg4CWyS46U+tetbuCR5fvClyr3+HaZjaVVvPg0m1sK6vlzv9uZE+YJpvhbDlonWvy0P6XjvHTG6pKJYGth2r4YOcRvnpyccj2D3dZNxhHDMyI6jxPfn02JUfrSUtx4hDB6zP4U9f+0J2bYfUc9d9EPX/aEN6xUzbRGD4wg/2VDXxlzmiuatUKZYB97qN1zbyx6RDjirIZU5AV5iyWsupGvhDU7PE7Z43n+FED+fpfV/P7N7byot20E6yOUm9tKetw6ICy6kZ+/O8NgbL2VxrclUoC5/7uHQCumDWKlKCelPXNHkSIuuv8aRMKAstOh+AztAR3u2bua3Wj8oLjhpKdnsJZk4po7ZGvnkiKU/jd69uYWZzH/KmDOWVcAU0eL2kpbTsqpbucDMpKZdfhOn77+laGDUhnxQ/Pbre8/1kX2gRz8tAciu0Pg0ht7CMJnnGpdWqpP9HgrlSCBbcKqW3yMDCzJZft9hpcDkeXgpSI1W7cf3b/GVq3kslOS+HC44aFPce5x1g3WedNDh1KIFxg9xuSm86HdpPGjnrSFuaktTzX1MHMnViI077W1hNa+5VVN1IUYRz2RreVq3/5htMjPndfpzl3pRLshn+03Kj8w5vbeGz5Lpo8VoDy+nyBm5Sd5RTBZ0zgw8OfB28d3GNdux06IJ2Soy3zkxpj+Mu7O7lh0UdtjvVf55IbT+eRK2eSm+4KtOMHq+nnV+eMZvltZ3FSsdUzd9Yv3qS2qW0zTr9lW8vJSU9h8pD+m28HDe5KJdyK7S1txh9/bzc/f3ETb262Ugtur+nypM0Ou7WMP9C+a7dNr21yM2VoLgDXnBb7IX0Ht2pbP+aHL3PXS5tZvL60Tdt1/wfNsFa58eL8TAA+d/xw/vfSaYzIy+Spa+YE9l9v9zxtraHZy4odR7h4+jAccZzsujfQ4K5Ugo0pyOLksflcefLowLa9FVazP4/P1+XRDB1i5dz/uWpfYNttz33Myp0VjMjL4KOfzue2BZO7V/gwhkZImbSucfvXs9NCM8T+NNHJdksegNQUB09cfRJg1c5bf1BUNbi54IF3afL4ODPM/YP+RoO7UglW2+QhJz2Fn18yjTdvOQOXUyirtjoMeX3dqLnbOffgWZv+udoK9MePGkheVmpchsHNC2r/7vebL0wHWsa++dwf3+PhZTuobfSQmepsc43XnzWep78xm5nFg0K2BwftumZvyL57lmwJDIA2NEzP3P5Gg7tSCfSLlzezxR5REWBcYTYj8jIpt4eotW6odjHn7hA8PkOz18ct8ycSfJpwLWNiZUhQzX39/5zLhz86m0x7ApCH397Bnop61u6t5J4lWyitaqAo6KaqX0aqk1PGFbTZDnDfF60PiuAeswDBn1MjB2V29zJ6PW0to1SCNHm8PPLOTgBODKqhFmanUV7TyIb9VW2GCOiM4BulBTlpvHXLmQzIcCFCSIucWDtn6mDmTx3M508YYbV7z3AFBhpr8vjYH3SzdcmGg5w9uXOTevhb2Byqbgy0oTfGIHZ7oI9+Oj/Q3r4/0+CuVIKs31cVWD5/Wsu4LkW5aXyyv4rb/vVxt84fXFPPTXcF2o/3hD9fOTNkPd3lZMbIgRypa2J/ZXBLGmt0y86YPCQXl1N4ZcNB5ozNp9HtZfJPXwGswB8uLdQfaVpGqQTxj/Xy2s1zQzouFednUXK0gY2l1e09NCqvb2qZqCIZarKjBmWyt6KekqOhY8Skd3LWpsKcNE4dX8DKnVYPW/90gdAyTo6KIriLyEgRWSoim0Vko4jcGOYYEZH7RWS7iHwsIifEp7hK9R31bi+pTkeb4WhH52cGOvCMHJTBitvnden8VwUNZZCbkfgv6aMGZbKvooGHlu4gNcXBqh+fw6ziQVw7d2ynzzUkNz0weYk/yAMh3wr6u2jecQ9wizFmrYjkAGtE5HVjzKagYxYAE+yf2cCf7N9KqXY0ub3MGDWwzfbgsVjOnza0TRvwaH3mmCHcaqd2Ruf3XEqmPUOCWrA0e3wU5qTxjD3jU2ftsUeILL79pZiUrS/qMLgbYw4AB+zlGhHZDAwHgoP7JcDfjNXwdKWIDBSRofZjlVJhNHp8YdMlwYE4v5P56GADMl1s+vln2HaoNinSMscMyw0sX3fGuG6dq6bJ3fFB/VynElQiUgwcD3zQatdwYF/Qeom9rfXjrxWR1SKyurw8+lHolOqLmtxe0sOMNR58g/Gzx4/o1nNkpqYwfWTbbweJcPyoPNbdMZ+VPzybH3xmUrfO9fsvHR+y/qvPH9fOkf1X1Ik4EckG/gXcZIxpfacnXEPcNqP+GGMeAR4BmDlzZmxnwlWql6lr9oS9mSgibL97ATWNnj7X8iNWTTDHF2UzfeRA1tuzN500ZhBvfG8uTZ6uz97U10QV3EXEhRXYnzLGPB/mkBJgZND6CKA0zHFKKcDt9bGvoqHdmnmK09HnAnus/fKzx/LXFbspyEll9KDMfj+WTGsdBnexekI8Cmw2xtzXzmGLge+IyD+wbqRWab5dqfb5h6XN7eQMS6rF1GG53HuZpmPaE81f1qnAV4FPRMQ/NumPgFEAxpiHgZeB84HtQD1wdeyLqlTf4U8fpPXT+T1V/EXTWmY54XPqwccY4PpYFUqpvuqdreW8sG5/oONNpEkvlOoO/U6oVA+68rEPQ9bTXFpzV/Ghf1lK9ZDmMC05NC2j4kX/spTqIUfqrCFqjw/qlTpjZF6iiqP6OA3uSvWQirpmAL45t6V35hCdVELFiebcleohjW4rLZOR6uS28yYzOl8nlFDxo8FdqR7iz7m7nMK3zuze2CpKdUTTMkr1kGavtm1XPUf/ypTqIf6ae6pT27ar+NPgrlQPcds191StuaseoH9lSnWCz2e44P53Kb79JZ5Zva/jBwQJzrkrFW8a3JXqhHUllYG5TW997mPW2UPOtuetLYc4ajeBDKRltOaueoD+lSnVCXVNnpD1Sx96D2topbbqmz187YnVLHzcGnKgSdMyqgfpX5lSndDQbA3VGzxl3Nq94Wvv/mPXl1QBLTX3NL2hqnqABnelOqHBHof9/iuOD0ztdri2KeKxAC98tL8l556iOXcVfxrcleoE/yQbGS4nJxbnhWxre2zLQGGr91S0tJZx6r+dij/9K1MqgupGNzf+4yOO2LXzt7aUAVZw93dGagoK4q9tPMhxd75KQ7OXxev2B7Y/uXIv972+FYdYU+gpFW86/IBSESxeV8p/1pXy3vbDfPijc3h14yEA0l1OvPaN1EaPVXPfc6SOa/++BoAr/rwybEuarDT9l1M9Q6sQSkWQY89xeri2mZKjDYHtaSkO0l3WjVF/WmbPkfrA/uDAPjRo5MeinLS4llcpPw3uSkUQPMHG3F8vDSw7HEK6nZbx59aP1jeHPUdBdktAP31CYTyKqVQbGtyViqC2Vbt2gDsunApYufMUh9Dk8XK0rplbn/uYFIdw+oSCkONzM1pSMbPHDIpvgZWyaXBXKoLaxrbB/WunjQksp6U4aHT7uPvlzTR5fHh8hkFZqSHH/+ziaYFlp0ObQaqeoXd3lIqgplXNfdE35oSsp7ucNLq91De3HHfv54/DZ+CmcyZQkJXGgEwXZ0wsZNnWclJ0XBnVQzS4KxVBTaua+8nj8kPWreDuw+uzWs5MHJxNusvJA1ccH3IJLDe/AAAe1ElEQVSc/0ZqTrorjqVVqoUGd6UiqGl0M3JQBrnpLq6dO7bN/jSXg0aPl5KjDUwoyubZb54S9jx3XnwMs8fmM3O0ToiteoYGd6UiqG3ykJeZyuLvnBZ2f3qKkw92VnC4tonvzhvPgMzwNfOstBQuO3FEPIuqVAi9oapUBLWNHrIjdDxKczkCY8ssPKW4h0qlVMc0uCsVQU2jJ9CRKZyd5XWB5fxs7aCkkocGd6UiqG3yRBwy4MxJVqek4QMzeqpISkVFg7tSETS6vWS42h9//YcLpgAg2sJRJRm9oapUBG6vD1eEURwH56bxtVPH8IWZerNUJRcN7kpF4PaaiBNaiwh3XDS1B0ukVHQ0LaOUreRoPR5vy0BhD761jQa3N2LNXalk1eFfrYg8JiJlIrKhnf1nikiViKyzf+6IfTGViq8jtU2cdu9S7nppc2Dbb17bCsCh6vDT6CmVzKJJyzwBPAj8LcIx7xpjLoxJiZRKgKP1bgCWbS1vs297eW1PF0epbuuw5m6MeQeo6IGyKJUwjy7fCYSfD7U+zLC/SiW7WCUTTxaR9SKyRESOae8gEblWRFaLyOry8rY1JKUSZdGH+wA4UNXIgaoGymoaA/sWTBuSqGIp1WWxaC2zFhhtjKkVkfOBF4AJ4Q40xjwCPAIwc+ZME4PnVirmTv7lW4Hlc6cO5qZzJiawNEp1Tbdr7saYamNMrb38MuASkYIOHqZUUgme5zTYfV+agUMn2FC9ULeDu4gMEbH654nILPucR7p7XqV6UkZq216oX5w5IuKgYUolsw7/ckVkEXAmUCAiJcD/AC4AY8zDwGXAt0TEAzQAlxtjNOWiepXgibDHFmRx8/yJXDR9WAJLpFT3dBjcjTFXdLD/Qaymkkr1WsHB/ewpRRrYVa+nXe+UApq9vkDefcvBmgSXRqnu0+DeBQ8v28FO7djSpzR7fJw63moHoLV21RdocO+kxetLuWfJFub9dlmii6K6odHt5Z4lW9h6yKqlN3t8FOWkseuX5/PFmSMTXDqluk+Deye9tflQoougYmD17qM8vGwH5/7uHf7y7k48PkNqigPRgdlVH9Frg3tFXTO/eHlzyI2weHjho/28uvFgYH1gZioAKdr2uVerbXIHlv2DhaWm9Np/B6Xa6LV/zb997VMeeWcnL39yIG7PYYzhpn+u45t/XxPYdrS+GYATRufF7XlV/NU2tR1DJlWH9lV9SK/toeFvSF/V4I54XHeUVrWML1JV7+ax93ax67A1IbLPp035e7P65raDgc0sHpSAkigVH72+qtLVFGlVvZvi21/i5//d1O4xNy76KLD8m9c+5Q9vbuPjkioAvK36aflv0O05Ute1AqkeVdtqpMeJg7OZMXJggkqjVOz12uDu7wTb1Zy7f4zux97b1W5APljdUnOvbPUNwduq5r50SxkPL9vBGb9+m4Zmb9ihY1Xy2F7W0pTVIfDf756WwNIoFXu9Mrj/8PlPAkO03vXSZqobO5+aqQuquZ3x67fDHlPd4CYv0wXArsNWMBiRl8G4wqyQ4F5e08SiVfsC61PueIXJP32FJo8G+GT1/Nr9geWhAzJIS2k7toxSvVmvDO6LPtwbsl5S0RDV47w+E6hR+2+M+m0vq+WjvUe59KH3aPJ42XOkjupGDyMHZQKwYX81X549iuW3zWNcYXYguL/4cSkn3f0G72wt5/hRoV/rb/rHui5dn4q/DJcVzM87ZggPffmEBJdGqdjrdTdUK4OC8sJTinlixW48vsipmf+s28+jy3fxcUkVDoGtdy3gaF1ocL/7pU0s/dSaQGTST14JbD9hVF4gz36a3YPR6ZBAcP/PutLAsXMnFPLUNbMRhPm/W8aSDQepqnczwK79q+QxKCuVOWPz+e0Xpye6KErFRa+rua/bVwnA09fM5oxJhQB4Omi58vCynYEA7TNW2uRQTeikx/7A3tpt500OLPtr8f7g7vb62HuknmnDc3n1prncePYEMlNTyEh18q0zxwFQXtsY9ryqZ/h8hjsXbwy0cgLweH2U1zRRkJOawJIpFV+9LrgPykrlshNHcOyIAbgcVvE93vDB/dKH3uPMXy8N6bAC4PYalm87HPYx184dG1i+/KSRZKQ6SXdZzzMqPyi4G+scnx6q4fKTRjFpSE7IpA5jC7IB2Fha3cUrVbGw60gdT6zYzTf+tjqwbW9FPc1eHxOKchJYMqXiq9elZY4bMZDffMHKbac4rWDq8YZPy/hr+eHsO1rP2IIsHv7qiTy5cg9/e38P86cO5kfnT+EHn5nE/W9u48uzRwPw16tnsfVQDbnpVnrFKYLHa9hWZo1LctFxbQeaOqk4j4GZLm78xzrOmFgY6Nmqela6nVsPvoG+9ZB1c3xCUXZCyqRUT+h1NfdgLju4u6PoUPSlmSP5wokjuO4MK11SWe8mLyuViYNzWHhKMdOG5/K/l0yzz+vglnMnMcQeAnb22Hy+enJx4FxOh7C/soH1JVXkZ6WGzamnOB1U1lvfGPwte1TP8w8TUd/c0nLpuietHsfFBVkJKZNSPaFXB3dnIC3TcVv3uRML+fUXpvPl2aMC2/ZW1AMwtjCbF797eiCYd+SkMVZPxpc+PsBoO1UTzo1nW/OEbyytiuq8KvZ8dn+I+mYPVQ3ukBvyuem97ourUlHr1X/d/lqZ/4bqO1vLeXT5LjaWVgXGCfnWmeO4+tRiCrPTAELmxCxvdVM1Wp8/YQS3PvcxQMR0y83zJ7K/soHn1pTwh8sNTh1srMf5OxK7vYbpP3uN333Jah0zrjBLR4BUfVqvDu4uO4C77Zr7lY992OaYU8blU5TTUiPPDqqtnT6hoEvP63QIr988lz++vYPvzhsf8djBudaHytuflnH2lMFdej7Vdb5Ww0Tc/M/1gPZIVX1frw7uRTlW4DxQ2RgI8KPzM/nfS6ZR1eBmb0V9oG26n8vpYFBWKieMGsgDV3S988qEwTn87kszOjzuqpOLeWjpDnaU12pwT4D2pmrPTO3Vf/pKdahX/4XnZaWS7nLwwa4K5k0pAuC78yYwd2JhxMet+ck5AD3ytbwoN53R+Zks2XCQb5w+VlMBSUCzY6o/6NXBHaDR7eONzYcC48uMKWj/BqdfTwfY/zdrFL9csoXy2qaQFJGKv+C0zMJTirl5/sQElkapntPrg7vfh7sqACjOT77mbf6erUdqmzW497DgtMydFx+TuIIo1cN6dVNIgJygG6QZLieDspKvs5C/TJE6Van4aH1DVan+otcH979+bVZgucHtTcqctj+4//D5T0J6Sqr484f2P1ze8c1vpfqSXh/cTxiVx8NfSe4hW/2tegBW7zkas/Ou2XOUfXZHLBWef1KXZPzQVyqeen1wBwJNDOeMTc45MAdmpvKf608FYFk7o092xef/tILTf7U0Zufri/xZGQ3tqr/pEzdUXU4Hu++5INHFiGja8AEANMZxdqaqBjc+nyEvCe87JIo/LePQmrvqZ/pEcO8NnA5h2ID0Ls/5Go2T7nqDZq8v6T/oepIvkJZJcEGU6mF9Ii3TW7hSHIGetLG08PEPqWvy0ByHc/d2/rSMdlxS/Y0G9x6U6oxPcH/703KO+Z9XA+u+KIZA7i9amkJqdFf9iwb3HuRyOuKalvGraDX5d38WuKGqsV31Mxrce5ArxUFzO1MCdsdF04dx5qRCZtnjzJdVd20o42RR2+Th7U/LAs0YY0FvqKr+psPgLiKPiUiZiGxoZ7+IyP0isl1EPhaR5G50nkBpTgfuGNXc/YHv2OEDuP/yGTxx9Sxu/cwkAMpqevek3L959VMWPr6Kd9uZ57YzAjdUu30mpXqXaGruTwDnRdi/AJhg/1wL/Kn7xeqbXCkSs5y7P60+f+rgQAcd/7g1d7+0Oaa13p5kjOGfq6xpCXcfqevUY59ZtY8N+0NnvQrcUNXvqKqf6fBP3hjzDlAR4ZBLgL8Zy0pgoIgMjVUB+xKX0xHSosXnM13OwXt81uOCZ3cqsicG2VZWS8nRhraP6QWtafZVNNDgtvoC1DR2bqiGW//1MRc+sDxkW0vNXevuqn+JRX1mOBA8A3SJva0NEblWRFaLyOry8tj11OwtUlvdUL3l2fVM/MmSwPquw3VRDyfgtavuKUHBPd3l5P++eiIAZTVNrNpdEThu84Fqxv94CW9uPtTt64in8tqWlNLh2ujvHQR/U/nS/73PX1fstrbb2zTlrvqbWAT3cP82YXMCxphHjDEzjTEzCwsjT6jRF7Vu5/7vj/YDVhA7WtfMWb95m/N+/05U52potmq3aSmhb+GQXCs188Bb2/jCw+/z8icHgJYxbd7cUta9i4izw7VWS5+sVCerdkf6whiqKehD84NdFfzP4o1868k1vG0P96Bjy6j+JhY9VEuAkUHrI4DSGJy3z0m10zLr9lWyvaw2sP3ulzZz8rh8AOqavVTVuxmQ6Yp4rqoGa3KS1hN0+0eg9Ae1g1VWTfjBt7YBoTX9ZHTEDu6XHD+cRR/upaKuOaphnP0fdsGWbDjIkg0HAb2hqvqfWNTcFwNX2q1m5gBVxpgDMThvn9Po9rKvooFLH3qP7z+7PrD93x/t57WNLemSm59Z1+G5Ku3g3vpDoDBoBEqA0qoGNpVWc8huHpmS5HcWKxus4H7BsUMxBj7cdSSqx/ln4mqPNoVU/U00TSEXAe8Dk0SkRES+LiLXich19iEvAzuB7cCfgW/HrbS9nDNMrfnezx8LwLKtZWSmOgF4a0sZTREGGCuraeSuFzcBMDAjNLinu5z8+cqZTB9hDVT2+Hu7+c6itYH9Kc7kDnJuj5XRKy6wZtSqqIsctP0++8cVgeVjhuW22a+xXfU3HaZljDFXdLDfANfHrER92M8uPoYXPw79UrPg2KHc9q9PcHsNI/PS2XnYav6390g9eVmpfPuptXy4q4LTJxTw5dmjGZjp4uFlO1i715rVaUBG2/TN/KmDmT91MMW3vwTAzvKWJoW56ck9Vpzb68PpEDJc1gddc5SjaFbUtfTKnTQkh42l1SH7dx+p49TxBbErqFJJLrn/0/uY/OzQlMlVJ48mN70lOO88XMelM4bxwrpSNh2opqy6KTA37LvbDgc69fhr5QBDB2R0+LxLbjyd8pomrnzsQ7LSonvL/75yD8X5mZw+oWdvfDd7fbicQqp9o7izg6Fdf9Y4vnPWBJ5fuz9ke5M7+ZuBKhVLGtwT5PGFJ3HW5KKQbf/31RM5e3IRL6wr5c7FG0MmIVm5s6XlSHbwvLF2KiecG+aNZ2xhNlOG5jJykNVm3BPF8Afby2r46QtWh+SeHj642eMj1ekg1ekIrHfG2VMGk5Hq5K1bzmBvRT0/eWEDJUcbmFmcF4/iKpW0NLj3sLe/fyYiMDo/K7Dt3VvPwhgYlZ8Z2Ha03s2HuyqYP3Uwf75yJrN/8Ubgpqgzypui3zt3UmA51elABGqimMN18fqW1JHPZ3D0UAubI7VNPLFiN9lpKbjsewOdDe7+dM7YwmzGFmaz/LZ5GGO0KaTqd5K76UQfVFyQFRLYAUYOygwJ7FefWgzA3op6TrGbSL7xvTO44ewJ1vYjdTgdwhvfmxv186amOCjOz2LrwZoOjz1Q2dK79ct/+YDKHhpl8o7FGwFr4DARKzXTFEVapr655QPLFeaGsQZ21R9pcE9CwR2dThhlpRNy0l2BDkq7j9TzueOHM74op1PnnTosl40Hqjo8Lvjm5Ps7j3D/m9s79TxdVd/qW0ValEMkVze0PC7Zm3oq1VP0PyEJnVTcMtH3lKEtzfqy0lry6+HGjunI2IIsSo42dDiomL+DlN/bn8a/V2tVg5sVO6w27YPtMXKimblq26Ea5vzyzcD68LyObzAr1R9ozj0JXTx9GJOG5HCktjnQagQgM7Xl7TpxdOdvEGalpWAMNLi9IedqrbrRzYAMVyDIu33xb2ny7afWBIYQuPUzk4G2Y/GEc92TawLLf7h8Bi6n1leUAq25JyURYfKQ3DbtsrOCWsb48/Kd4W8GWdvBTdWqBjdTg74xxDPVUXK0noZmL+9tb+mJ+vkTRwDWfYJnVpeEDNUQrqw9UU6lehv9b+hFgseRcaV0/q3LttM6dU1Wx6A7F2/kkgeXc6TV6IvVDR4mDWnJ53vjNCerz2c47d6lTLnjlbD7/TdHL7j/3XbPETymTLL3vlWqJ2lw70WCW9SkdiH9kGWnYs76zdt8tPcoT6zYzfqSKk7/1VKMMdyzZAu3/+tjGtzekDFq4hXcy8MM6Rv87cSfpmmKkJq59PiW0aXDtZRRqr/SnHsvkh3Uu7QrwT24t2fwWCz1zV42llbz8LIdgW0zRg7kn9fO4Z5XtnCgMj7T9lW3unF75cmj+fwJIwLrdVG0yfcF3RzWtIxSLfS/oZfqSseiSEMPBM9gtPCUYk4dX8DssflMHpKLJ4Y19+ufXsuxd74KWB8qwb47bwLTRw4MrPvvDWRG6IWraRmlwtPg3o+cObGQP33Zmr/c5RTW/nQ+z3/7lJBj1t0xnzsvPiaw7nSE1o6766WPDwSmz6trDq2ZF2SHjtvutodKSHe1H9wbg8aMKWw1do9S/ZmmZXqZv399VkjLks4QERYcO5Ttdy/AIYLDIQzKSg00e3z86pPaTP6R4nC0mXt1w/4qRudnkpMeeUKRYJsPVPPf9S1zuBhj+Nlia9jiguw0Dtc2tduT1N8ccvXuCqaPHBjS3LHB7WX6iAE89Y05IWkrpfo7/W/oZU6fUNjtkRpTWuXrX//eXLYcqGHuxLbndYgQnJXx+gwXPrCcWcWDeOa6k6N+zh88t54N+1uG4d1YWk2z10e6y8HKH86L+FgROFDVwGUPv8/njh/OfV+aEdjX6PaS7nJqYFeqFU3LKIpy0sMGdrDy2MGtZfyplA87Mb8pQF6rbwSllQ3UNLr53AkjSHE62nzghJTBIYHmm89/FDqUb1lNE/nZHU/Dp1R/o8FdReSQVsE9ihYs4bRO96zYcYTKejd5EeaK9c+o5PYafvzvT9rsb3R72X2kjomDOzfGjlL9gQZ3FZHTAV4THNxbWqd0ZjjeyvpmHAITirKZOjSXJ1fuweMzjC3Ibvcxz113ClfMGkltk4cPdrV8U6ix50vdXlaLMWhwVyoMDe4qorQUJ16fCQTy4Jp7uE5I7Tla38wZEwt5/XtnMHJQRqB5ZaRmjhmpTgpz0tts/+1rWwHYesgavliDu1JtaXBXEeVlWemUiT9ZwoGqhpDgfrAq+s5NR+vcgXO9uvFQYHukZo4AaWGGWfCPL7/nSD0iMGpQZptjlOrvNLiriPKzWnLlH+2tDBl0rKw6NLiXVTfy6saDbc5hjKGirrnNTVUIH7yDZYQJ/v4OXH94cxvZqSkhI2cqpSz6X6Eiah2QgzseHWoV3Bc+vopv/n0Nje7Qnqf7KhpocHsZU2DNQPXk12cH9kVqJQOh49n7x3n3+gybSq1mldFMG6hUf6TBXUVUlBva6/O/QfOrHqoJzbmXVlkTiASPGbN0Sxlzf70UgONHWUMLnDo+n2OHDwBaAnZ7jhsxILD816/NAqyOVWU18RnvRqm+Qnt+qIiK87PISUuhpsmD2+vjrS3WrEyDslI51CrnnuFyUombqgY3RfaUgFc/sSqwf5J941NE+O93T6OuyRNxvBsIHQ9n8pBc5k8dzKrdFYEPikXfmNP9i1SqD9Kau4rI6RBevdmaiDt4oK/R+ZlsazWJRobd8qW6MXS0R4AxBVltUjAdBfZwZo8ZxN6Kep5cuQenQ5g1ZlDHD1KqH9LgrjrkD8J1TR4G56Zx8fRhZKY6+WR/Fb6gDk47y+sAuOqxVRhjQuY/vfHsCTEpS3G+lbffcrCGsQVZOLswOqZS/YEGd9Uhf1v0+mYvXp8hJz0lMA1fk8dHk8cbaJ4I1lC9eyvqORq0LVJ79s4IHmpgwbFDY3JOpfoizbmrDrmcDlJTHNQ1eWj2+HA5HRTYw+vuKK/lysc+pKKuOeQxH5dUBYYKPn1CAedMGRyTsgRP7J2jg4Up1S7971BRyU5Loa7Zg8dncDmFrYesfPvVT6xqE9gBPtlfxSPv7ATg9gWTuzS5SDhjC7MCy0MHtu29qpSyaHBXUamoa+bJlXsBqybvr5WXt2oOefdnp/GzxZtYt7cysG1kDHuQupwOPrnzXA5UNTKhqP1xaZTq7zTnrqKy8JTiwLLL6eDauWPbHDM6P5Mvzx7NzOI8dh+xbq5+5pjB5HZiUo9w3r31LJ4LGjs+J93FxME57U7uoZTS4K6idOfFxzAiLwOA1BQHU4bm8pcrZ4YcM2yAtX9gposyu0Z/2Ykju/3cIwdlMrNYmzwq1RlRBXcROU9EPhWR7SJye5j9C0WkXETW2T/XxL6oKtH848C47Imova3mVvWP8ZKW0tIyZmCE8dqVUvHTYc5dRJzAQ8B8oARYJSKLjTGbWh36T2PMd+JQRpUk/HOX+n+bVsF9XKGVA/930GxJAzM0uCuVCNHU3GcB240xO40xzcA/gEviWyyVjPwdhvw9TeeMzQ/sO2fKYG5bMAmAh79yYmB76xmYlFI9I5rgPhzYF7ReYm9r7fMi8rGIPCciYROtInKtiKwWkdXl5eVdKK5KJH9aJtVOywzMTOWzx1t/ChccNySQjjlv2pDAYwZozV2phIimKWS4Jgmm1fp/gUXGmCYRuQ74K9BmSntjzCPAIwAzZ85sfQ6V5MYWZrN2byWN7pZhBW5fMBkRWDAttLfoQ//vBHaW1+pY60olSDTBvQQIromPAEqDDzDGHAla/TNwb/eLppLN9JEDeW5NScg47oNz07nvizPaHHvBcTo0gFKJFE1wXwVMEJExwH7gcuD/BR8gIkONMf6Bvi8GNse0lCopfHHmCEqO1nPN6W3buCulkkuHwd0Y4xGR7wCvAk7gMWPMRhH5ObDaGLMYuEFELgY8QAWwMI5lVgmSluLkhwumJLoYSqkoSOvmbD1l5syZZvXq1Ql5bqWU6q1EZI0xZmZHx+ndLqWU6oM0uCulVB+kwV0ppfogDe5KKdUHaXBXSqk+SIO7Ukr1QRrclVKqD0pYO3cRKQf2dPHhBcDhGBanN9Br7h/0mvuH7lzzaGNMYUcHJSy4d4eIrI6mEX9fotfcP+g19w89cc2allFKqT5Ig7tSSvVBvTW4P5LoAiSAXnP/oNfcP8T9mntlzl0ppVRkvbXmrpRSKgIN7kop1QclRXAXkZEislRENovIRhG50d4+SEReF5Ft9u88e/tkEXlfRJpE5PthzucUkY9E5MWevpZoxfKaRWS3iHwiIutEJGkHyY/xNQ+0J2PfYp/v5ERcU0didc0iMsl+f/0/1SJyU6KuK5IYv8832+fYICKLRCQ9EdfUkRhf84329W7s1ntsjEn4DzAUOMFezgG2AlOBXwG329tvB+61l4uAk4C7ge+HOd/3gKeBFxN9bT1xzcBuoCDR19TD1/xX4Bp7ORUYmOjri/c1B53TCRzE6syS8GuM1zUDw4FdQIa9/gywMNHXF+drngZsADKxZsp7A5jQlTIlRc3dGHPAGLPWXq7BmoN1OHAJ1j8x9u9L7WPKjDGrAHfrc4nICOAC4C89UPQui+U19xaxumYRyQXmAo/axzUbYyp75CI6KU7v89nADmNMV3t4x1WMrzkFyBCRFKyAVxrn4ndJDK95CrDSGFNvjPEAy4DPdqVMSRHcg4lIMXA88AEw2NgTb9u/i6I4xe+BWwFfnIoYczG4ZgO8JiJrROTaeJUzlrp5zWOBcuBxO/32FxHJimNxYyIG77Pf5cCiWJcvHrpzzcaY/cBvgL3AAaDKGPNaPMsbC918nzcAc0UkX0QygfOBkV0pR1IFdxHJBv4F3GSMqe7C4y8Eyowxa2JeuDjp7jXbTjXGnAAsAK4XkbkxK2AcxOCaU4ATgD8ZY44H6rC+8iatGL3PiEgqcDHwbKzKFi8x+H/Ow6r5jgGGAVki8pXYljK2unvNxpjNwL3A68ArwHrA05WyJE1wFxEX1ovylDHmeXvzIREZau8fCpR1cJpTgYtFZDfwD2CeiDwZpyJ3W4yuGWNMqf27DPg3MCs+Je6+GF1zCVBijPnAXn8OK9gnpVi9z7YFwFpjzKHYlzR2YnTN5wC7jDHlxhg38DxwSrzK3F0x/H9+1BhzgjFmLlABbOtKeZIiuIuIYOVPNxtj7gvatRi4yl6+CvhPpPMYY35ojBlhjCnG+ur6ljEmKT/pY3XNIpIlIjn+ZeBcrK92SSeG7/NBYJ+ITLI3nQ1sinFxYyJW1xzkCpI8JRPDa94LzBGRTPucZ2PlspNOLN9nESmyf48CPkdX3+9430WO5gc4DStv/DGwzv45H8gH3sT65HoTGGQfPwSr9lYNVNrLua3OeSbJ3VomJteMlX9eb/9sBH6c6GvrifcZmAGsts/1ApCX6OvrgWvOBI4AAxJ9XT14zT8DtmBVWP4OpCX6+nrgmt/FqqysB87uapl0+AGllOqDkiIto5RSKrY0uCulVB+kwV0ppfogDe5KKdUHaXBXSqk+SIO7Ukr1QRrclVKqD/r/aU85N+DJHA4AAAAASUVORK5CYII=\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 92,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot histogram\n",
        "plt.title('Stock Box-Cox Power Transformation in Histogram')\n",
        "plt.hist(df['boxcox'])\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 93,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    }
  ],
  "metadata": {
    "kernel_info": {
      "name": "python3"
    },
    "language_info": {
      "nbconvert_exporter": "python",
      "version": "3.5.5",
      "mimetype": "text/x-python",
      "name": "python",
      "codemirror_mode": {
        "version": 3,
        "name": "ipython"
      },
      "file_extension": ".py",
      "pygments_lexer": "ipython3"
    },
    "kernelspec": {
      "name": "python3",
      "language": "python",
      "display_name": "Python 3"
    },
    "nteract": {
      "version": "0.14.4"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}